### [hal-01983440] A TOPOLOGICAL STUDY OF PLANAR VECTOR FIELD SINGULARITIES A tribute to Ivar Bendixson

18 janvier 2019

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Une partie des prépublications de l’Institut de Mathématiques de Bourgogne est disponible dans la collection HAL du laboratoire.

Ci-dessous les derniers dépôts des membres de l’IMB :

18 janvier 2019

In this paper one extends results of Bendixson [B] and Dumortier [D] about the germs of vector fields with an isolated singularity at the origin of IR 2 , not accumulated by periodic orbits. As new tool, one introduces minimal curves, which are curves surrounding the origin, with a minimal (...)

4 janvier 2019

In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

19 décembre 2018

In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a (...)

5 décembre 2018

In this paper we construct a family of cohomology classes on the moduli space of stable curves generalizing Witten's $r$-spin classes. They are parameterized by a phase space which has one extra dimension and in genus $0$ they correspond to the extended $r$-spin classes appearing in the (...)

26 novembre 2018

We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, (...)

16 novembre 2018

We study the structure and the Lyapunov exponents of the equilibrium measure of endomorphisms of $\mathbb P^k$ preserving a fibration. We extend the decomposition of the equilibrium measure obtained by Jonsson for polynomial skew products of $\mathbb C^2$. We also show that the sum of the (...)

30 octobre 2018

We provide a complete description of normal affine algebraic varieties over the real numbers endowed with an effective action of the real circle, that is, the real form of the complex multiplicative group whose real locus consists of the unitary circle in the real plane. Our approach builds on (...)

23 octobre 2018

We show that any free product of two (non-trivial) countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN extensions or free products, amalgamated over a finite group, admit such an action and we extend (...)

27 septembre 2018

This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled Workshop for young researchers: Groups acting on manifolds held in Teresópolis, Brazil in June 2016. The course introduced a number of classical tools in smooth ergodic theory-particularly (...)

26 septembre 2018

Mathématiques en France, Mathématiques en Allemagne à la fin du XIXe siècle : témoignage du mathématicien belge Alphonse Demoulin. travail en cours, Septembre 2018

25 septembre 2018

We study quasi-normal modes of black holes, with a focus on resonant (or quasi-normal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild (...)

11 septembre 2018

The Sagnac effect can be described as the difference in travel time between two photons traveling along the same path in opposite directions. In this paper we explore the consequences of this characterisation in the context of General Relativity. We derive a general expression for this time (...)

11 septembre 2018

Light rays propagating in opposite directions around the same loop in general show a relative phase shift when recombined. This phenomenon is known as the Sagnac effect after Georges Sagnac who, in 1913, demonstrated with an interferometer on a rotating table that the phase shift depended on (...)

7 septembre 2018

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions called solutions of order N depend on 2N − 1 parameters. They can also be written as a quotient of two (...)

5 septembre 2018

We study the equivariant real structures on complex horospher-ical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of such real structures and determine the number of (...)

30 août 2018

Let VB_n be the virtual braid group on n strands and let S_n be the symmetric group on n letters. Let n, m ∈ N such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to S_m , from S_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to (...)

6 août 2018

In biomechanics, recent mathematical force-fatigue models allow to predict the muscular response to functional electric stimulations and this opens the road to compute optimized electrical pulses trains. Such pulses are modeled as Dirac pulses and this leads to a sampled-data control problem. (...)

1er août 2018

Using a new quantization scheme, we construct approximate semi-classical Bergman projections on weighted L² spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic (...)

29 juillet 2018

In our previous paper [1] we have obtained, for the XXX spin-1/2 Heisenberg open chain, new determinant representations for the scalar products of separate states in the quantum separation of variables (SoV) framework. In this article we perform a similar study in a more complicated case: the (...)

16 juillet 2018

We construct smooth rational real algebraic varieties of every dimension ≥ 4 which admit infinitely many pairwise non-isomorphic real forms.

6 juillet 2018

By introducing a key combinatorial structure for words produced by a Variable Length Markov Chain (VLMC), the longest internal suffix, precise characterizations of existence and uniqueness of a stationary probability measure for a VLMC chain are given. These characterizations turn into (...)

3 juillet 2018

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

3 juillet 2018

The main result of this article is to construct infinite families of non-equivalent equivariant real forms of linear C*-actions on affine four-space. We consider the real form of C* whose fixed point is a circle. In [F-MJ] one example of a non-linearizable circle action was constructed. Here, (...)

25 juin 2018

We prove that the minimum-time controlled Kepler problem is not meromorphically Liouville integrable on the Riemann surface of its Hamiltonian.

21 juin 2018

The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse recovery performance. How can this be explained? To answer this question, we define several notions of " best (...)

8 juin 2018

The modular data of a modular category C, consisting of the S-matrix and the T-matrix, is known to be a incomplete invariant of C. More generally, the invariants of framed links and knots defined by a modular category as part of a topological quantum field theory can be viewed as numerical (...)

8 juin 2018

We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (...)

5 juin 2018

In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim at solving monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for the values (...)

4 juin 2018

We interpret geometrically the torsion of the symmetric algebra of the ideal sheaf of a zero-dimensional scheme Z defined by n + 1 equations in an n-dimensional variety. This leads us to generalise a formula of A.Dimca and S.Papadima in positive characteristic for a rational transformation with (...)

4 juin 2018

Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on (...)

29 mai 2018

We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean line into the real euclidean plane. We consider these up (...)

23 mai 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

15 mai 2018

Motivated by the general question of existence of open A1-cylinders in higher dimensional pro-jective varieties, we consider the case of Mori Fiber Spaces of relative dimension three, whose general closed fibers are isomorphic to the quintic del Pezzo threefold V5 , the smooth Fano threefold of (...)

15 mai 2018

We provide a locally free resolution of the projectivized symmetric algebra of the ideal sheaf of a zero-dimensional scheme defined by n + 1 equations in an n-dimensional variety. The resolution is given in terms of the resolution of the ideal itself and of the Eagon-Northcott complex of the (...)

4 mai 2018

The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the slender body approximation for Stokes (...)

2 mai 2018

In a Hilbert space $\mathcal H$, we study the convergence properties of a class of relaxed inertial forward-backward algorithms. They aim to solve structured monotone inclusions of the form $Ax + Bx \ni 0$ where $A:\mathcal H\to 2^\mathcal H$ is a maximally monotone operator and $B:\mathcal (...)

30 avril 2018

In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

27 avril 2018

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

27 avril 2018

The objective of this article is to make the analysis of the muscular force response to optimize electrical pulses trains using Ding et al. force-fatigue model. A geometric analysis of the dynamics is provided and very preliminary results are presented in the frame of optimal control using a (...)

27 avril 2018

The objective of this article is to make the analysis of the muscular force response to optimize electrical pulses trains using Ding et al. force-fatigue model. A geometric analysis of the dynamics is provided and very preliminary results are presented in the frame of optimal control using a (...)

26 avril 2018

The objective of this article is to make the analysis of the muscular force response to optimize electrical pulses trains using Ding et al. force-fatigue model. A geometric analysis of the dynamics is provided and very preliminary results are presented in the frame of optimal control using a (...)

26 avril 2018

In this article, we analyze the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

23 avril 2018

We study pseudo-abelian integrals associated with polynomial deformations of Dar-boux systems having a cuspidal singularity. Under some hypothesis we prove local boundedness of the number of their zeros.

21 avril 2018

Let $\Gamma$ be a Coxeter graph, let $W$ be its associated Coxeter group, and let $G$ be a group of symmetries of $\Gamma$. Recall that, by a theorem of Hée and M\"uhlherr, $W^G$ is a Coxeter group associated to some Coxeter graph $\hat \Gamma$. We denote by $\Phi^+$ the set of positive (...)

9 avril 2018

In a Hilbert space $\mathcal H$, we study the convergence properties when $t \to + \infty$ of the trajectories of the second-order differential equation\beginequation* \mbox(IGS)_\gamma \quad \quad \ddotx(t) + \gamma(t) \dotx(t) + \nabla \Phi (x(t))=0,\endequation*where $\nabla\Phi$ is the (...)

9 avril 2018

In a Hilbert space setting, we study the asymptotic behavior, as time $t$ goes to infinity, of the trajectories of a second-order differential equation governed by the Yosida regularization of a maximally monotone operator with time-varying positive index $\lambda(t)$. The dissipative and (...)

27 mars 2018

We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group Γ has the fixed point property FW for walls (e.g. if it has property (T)), every aperiodic action of Γ by diffeomorphisms that are of class C r with countably many (...)

16 mars 2018

We construct in this paper, rational solutions as a quotient of two determinants of order 2N = 14 and we obtain what we call solutions of order N = 7 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 112 in x, y and t depending on 12 parameters. The maximum (...)

16 mars 2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

7 mars 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

2 mars 2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

2 mars 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

27 février 2018

Affine control problems arise naturally from controlled mechanical systems. Building on previous results [2, 8], we go one step further and prove that the extremal flow given by Pontrjagin maximum principle can be stratified. We also study the regularity of this flow in terms of (...)

16 février 2018

In a Hilbert space $\mathcal H$, given $A:\mathcal H\to 2^\mathcal H$ a maximally monotone operator, we study the convergence properties of a general class of relaxed inertial proximal algorithms. This study aims to extend to the case of the general monotone inclusion $Ax \ni 0$ the (...)

6 février 2018

We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of (...)

5 février 2018

We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov (...)

10 janvier 2018

We prove that the minimum-time controlled Kepler problem is not meromorphically Liouville integrable on the Riemann surface of its Hamiltonian.

4 janvier 2018

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

3 janvier 2018

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

27 décembre 2017

We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of super-rigid affine Fano (...)

13 décembre 2017

This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian (...)

11 décembre 2017

In a Hilbert space $\mathcal H$, we study the convergence properties when $t \to + \infty$ of the trajectories of the second-order differential equation \beginequation* \mbox(IGS)_\gamma \quad \quad \ddotx(t) + \gamma(t) \dotx(t) + \nabla \Phi (x(t))=0, \endequation* where $\nabla\Phi$ is the (...)

8 décembre 2017

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as Lévy walks for which the persistence times depend on some internal Markov chain: they admit Markov random walk skeletons. A (...)

6 décembre 2017

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

5 décembre 2017

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

28 novembre 2017

28 novembre 2017

In a Hilbert space setting, we study the asymptotic behavior, as time $t$ goes to infinity, of the trajectories of a second-order differential equation governed by the Yosida regularization of a maximally monotone operator with time-varying positive index $\lambda(t)$. The dissipative and (...)

27 novembre 2017

Here we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We verify that the maximum of modulus of these solutions at order 6 is equal to 2(2N + 1) 2 = 338. We study the (...)

23 novembre 2017

In this article, we provide a comparative geometric and numerical analysis of optimal strokes for two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [31]) and the long-standing three-link Purcell swimmer [29]. The (...)

23 novembre 2017

Based on copepod observations, Takagi proposed a model to interpret the swimming behavior of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an (...)

31 octobre 2017

We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)

27 octobre 2017

An algebraic variety is called $\mathbbA^1$-cylindrical if it contains an $ \mathbbA^1$-cylinder, i.e. a Zariski open subset of the form $Z\times\mathbbA^1$ for some algebraic variety $Z$. We show that the generic fiber of a family $f:X\rightarrow S$ of normal $\mathbbA^1$-cylindrical varieties (...)

23 octobre 2017

In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing , if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a (...)

20 octobre 2017

In this paper we provide the complete classification of $\mathbbP^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic (...)

20 octobre 2017

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and (...)

20 octobre 2017

We prove structure theorems for algebraic stacks with a reductive group action and a dense open substack isomorphic to a horospherical homogeneous space, and thereby obtain new examples of algebraic stacks which are global quotient stacks. Our results partially generalize the work of (...)

5 octobre 2017

In this paper, we go on with the study of rational solutions to the Kadomtsev-Petviashvili equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials of degree 60 in x, y and t depending on 8 parameters. The maximum modulus of these solutions at order 5 is (...)

28 septembre 2017

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic (...)

25 septembre 2017

Let A be an Artin group. A partition P of the set of standard generators of A is called admissible if, for all X, Y ∈ P , X = Y , there is at most one pair (s, t) ∈ X × Y which has a relation. An admissible partition P determines a quotient Coxeter graph Γ/P. We prove that, if Γ/P is either a (...)

21 septembre 2017

The Functional Electrical Stimulation (FES) is used in the case of neurological disorders (paralyzed muscles) or the muscle reinforcement (sportsmen). A recent model was proposed coupling a force model and a fatigue model. Based on the specific structure of the model, we present a predictive (...)

7 septembre 2017

We discuss actions of free groups on the circle with “ping-pong” dynamics, i.e. dynamics determined by a finite amount of combinatorial data. As a natural extension of the work started in (Mann, Rivas, 2016), we show that the free group $F_n$ admits an isolated circular order if and only if n is (...)

29 août 2017

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose (...)

22 août 2017

We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)

21 août 2017

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that (...)

11 août 2017

We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)

9 août 2017

Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular (...)

1er août 2017

Let N be a compact, connected, non-orientable surface of genus ρ with n boundary components, with ρ ≥ 5 and n ≥ 0, and let M(N) be the mapping class group of N. We show that, if G is a finite index subgroup of M(N) and ϕ : G → M(N) is an injective homomorphism, then there exists f ∈ M(N) such that (...)

27 juillet 2017

Motivated by the study of the structure of algebraic actions the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X → X//Ga restrict to principal homogeneous bundles over the complement of a smooth point of the quotient. We (...)

25 juillet 2017

The Johnson filtration of the mapping class group of a compact, oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface. Each term of the Johnson filtration admits a Johnson homomorphism, whose kernel (...)

24 juillet 2017

18 juillet 2017

Ghys and Sergiescu proved in the $80$s that Thompson's groups $F$ and $T$ admit actions by $C^\infty$ diffeomorphisms of the interval. They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of (...)

17 juillet 2017

This article is inspired by two milestones in the study of non-minimal group actions on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves, and Ghys' freeness result in real-analytic regularity. Our first result concerns groups of real-analytic diffeomorphisms with (...)

13 juillet 2017

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on R d. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidth is selected by a method inspired (...)

5 juillet 2017

The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic (...)

29 juin 2017

Following recent success on the analysis of the Slope estimator, we provide a sharp oracle inequality in term of prediction error for Graph-Slope, a generalization of Slope to signals observed over a graph. In addition to improving upon best results obtained so far for the Total Variation (...)

20 juin 2017

Ghys and Sergiescu proved in the $80$s that Thompson's groups $F$ and $T$ admit actions by $C^\infty$ diffeomorphisms of the interval. They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of (...)

2 juin 2017

We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (...)

22 mai 2017

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that (...)

19 mai 2017

Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For (...)

16 mai 2017

We prove that even Artin groups of FC type are poly-free and residually finite.

25 avril 2017

Based on copepod observations, Takagi proposed a model to interpret the swimming behavior of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an (...)

14 avril 2017

We give a criterion for a flat fibration with affine plane fibers over a smooth scheme defined over a field of characteristic zero to be a Zariski locally trivial $\mathbbA^2$-bundle. An application is a positive answer to a version of the Dolgachev-Weisfeiler Conjecture for such fibrations: a (...)

12 avril 2017

The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , (...)

12 avril 2017

We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)

24 mars 2017

We go on with the study of the solutions to the focusing one dimensional nonlinear Schrödinger equation (NLS). We construct here the thirteen's Peregrine breather (P13 breather) with its twenty four real parameters, creating deformation solutions to the NLS equation. New families of (...)

8 mars 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

16 février 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

16 février 2017

This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a (...)

16 février 2017

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic (...)

15 février 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

6 février 2017

30 janvier 2017

In this article, we provide a comparative geometric and numerical analysis of optimal strokes for two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [31]) and the long-standing three-link Purcell swimmer [29]. The (...)

23 janvier 2017

In [17], based on the observation of copepods, Takagi proposed a model to analyze the swimming of microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and they are compared with the concept of efficiency. Our aim is to provide an (...)

7 janvier 2017

A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its etale endomorphisms are proper. We study the equivariant version of the conjecture for ℚ-acyclic surfaces of negative Kodaira dimension and infinite algebraic groups. We show that it holds for groups other than ℂ∗, (...)

8 décembre 2016

We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated (...)

8 décembre 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for l1 regularization, we develop an approach re-fitting the results of standard methods (...)

1er décembre 2016

We give a complete and unified description – under some stability assumptions – of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we highlight a phase transition phenomenon with respect to the (...)

1er décembre 2016

Minimum time control of slow-fast systems is considered. In the case of only one fast angle, averaging techniques are available for such systems. The approach introduced in Dargent (2014) and Bombrun et al. (2013) is recalled, then extended to time dependent systems by means of a suitable (...)

30 novembre 2016

The goal of this paper is to show how non-parametric statistics can be used to solve chance-constrained optimization and optimal control problems by reformulating them into deterministic ones, focusing on the details of the algorithmic approach. We use the Kernel Density Estimation method to (...)

28 novembre 2016

Let $(W,S)$ be a Coxeter system, let $G$ be a group of symmetries of $(W,S)$ and let $f : W \to \GL (V)$ be the linear representation associated with a root basis $(V, \langle .,. \rangle, \Pi)$. We assume that $G \subset \GL (V)$, and that $G$ leaves invariant $\Pi$ and $\langle .,. \rangle$. (...)

22 novembre 2016

For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the scale corresponding to the interparticle distance, in (...)

10 novembre 2016

We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane consisting of birational endomorphisms restricting to (...)

3 novembre 2016

In this paper we consider the degeneracies of the third type. More exact, the perturbations of the Darboux integrable foliation with a triple point, i.e. the case where three of the curves P i = 0 meet at one point, are considered. Assuming that this is the only non-genericity, we prove that (...)

28 octobre 2016

Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which (...)

28 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

27 octobre 2016

In this paper we consider the degeneracies of the third type. More exact, the perturbations of the Darboux integrable foliation with a triple point, i.e. the case where three of the curves P i = 0 meet at one point, are considered. Assuming that this is the only non-genericity, we prove that (...)

25 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

25 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

13 octobre 2016

The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirich-let problem for Laplace's equation, its (...)

5 octobre 2016

We construct algebraic families of exotic affine 3-spheres, that is, smooth affine threefolds diffeomorphic to a non-degenerate smooth complex affine quadric of dimension 3 but non algebraically isomorphic to it. We show in particular that for every smooth topologically contractible affine (...)

15 septembre 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for l1 regularization, we develop an approach re-fitting the results of standard methods (...)

13 septembre 2016

For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the scale corresponding to the interparticle distance, in (...)

2 septembre 2016

In control theory, the term chattering is used to refer to strong oscillations of controls, such as an infinite number of switchings over a compact interval of times. In this paper we focus on three typical occurences of chattering: the Fuller phenomenon, referring to situations where an (...)

30 août 2016

Qui est donc Alexandre Véronnet ? Nous allons voir qu'Alexandre Véronnet est un scientifique tout à fait étonnant ayant eu un parcours particulièrement original. Prêtre, il quitte l’Eglise à la fin de la Première Guerre mondiale. Il soutient une thèse en Astronomie en 1912. Le premier conflit mondial, (...)

3 août 2016

In this article, we make a comparative geometric and numeric analysis of the optimal strokes at low Reynolds number using two specific rigid links swimmers: the Copepod swimmer, a symmetric swimmer introduced recently 30 and the historical three-link Pur-cell swimmer 27 where the cost to (...)

22 juillet 2016

This paper extends recent results by the first author and T. Pock (ICG, TU Graz, Austria) on the acceleration of alternating minimization techniques for quadratic plus nons-mooth objectives depending on two variables. We discuss here the strongly convex situation, and how " fast " (...)

8 juillet 2016

In this paper we conjecture that the Links-Gould invariant of links, that we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular it seems to give a lower bound for the genus of links and to provide a criterion for fiberedness of (...)

4 juillet 2016

We show that a del Pezzo fibration π : V → W of degre d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of π is isomorphic to Z × A 1 K for some quasi-projective variety Z defined over the function field K of W , if and only if d ≥ 5 and π : V → (...)

30 juin 2016

The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solution to the nonlinear Schr\"odinger (NLS) equations. We first address the modulational instability of the (...)

20 juin 2016

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions called solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we (...)

20 juin 2016

We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator (...)

20 juin 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Extending ideas that emerged for l1 regularization, we develop an approach that can help re-fitting the results of (...)

10 juin 2016

In this article, we make a comparative geometric and numeric analysis of the optimal strokes at low Reynolds number using two specific rigid links swimmers: the Copepod swimmer, a symmetric swimmer introduced recently 28 and the historical three-link Pur-cell swimmer 25 where the cost to (...)

9 juin 2016

Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity, or by considering the super Hopf algebra $U_q (...)

9 mai 2016

We consider the orbital stability of the relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and (...)

8 avril 2016

We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerhäuser-Zhu that involves a sum over all group elements satisfying a certain condition, our formula (...)

7 avril 2016

The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation (...)

7 avril 2016

— The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

25 mars 2016

14 mars 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

11 mars 2016

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

11 mars 2016

The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

4 mars 2016

We show a simple and easily implementable solution to the word problem for virtual braid groups.

1er mars 2016

Given a symmetric non degenerated bilinear form b on a vector space V , G. Pinczon and R. Ushirobira defined a bracket , on the space of multilinear skewsymmetric forms on V. With this bracket, the quadratic Lie algebra structure equation on (V, b) becomes simply Ω, Ω = 0. We characterize (...)

23 février 2016

In the note added in proof of the seminal paper [Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebin and Marsden introduced the so-called correct Laplacian for the Navier-Stokes equation on a compact Riemannian manifold. In the spirit of (...)

23 février 2016

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a (...)

13 février 2016

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions (...)

8 février 2016

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon (...)

25 janvier 2016

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon (...)

13 janvier 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

7 janvier 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

22 décembre 2015

Qui est donc Alexandre Véronnet ? C'est à cette question que nous allons répondre. Nous allons voir que Alexandre Véronnet est un scientifique tout à fait étonnant ayant eu un parcours particulièrement original.

15 décembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

15 décembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

1er décembre 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

30 novembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

6 novembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

21 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

20 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

6 octobre 2015

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

25 septembre 2015

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbbC^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their (...)

22 septembre 2015

Estimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment... This question has been widely treated but new efficient methods are always welcome; especially if they (...)

13 septembre 2015

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or (...)

11 septembre 2015

The purpose of this work is to establish a counterpart for the Navier-Stokes equation of Brenier's generalized flows for the Euler equation. We introduce a class of semi-martingales on a compact Riemannian manifold which will be generalized solutions of the Navier-Stokes equation. We prove that (...)

4 septembre 2015

The purpose of this note is to establish a probabilistic representation formula for Navier–Stokes equations on a compact Riemannian manifold. To this end, we first give a geometric interpretation of Constantin and Iyer's representation formula for the Navier–Stokes equation, then extend it to a (...)

4 septembre 2015

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a recent work of A. Naber on the characterization of the (...)

1er septembre 2015

In [8], we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane $\mathbbR^2$. Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this (...)

8 août 2015

We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to (...)

23 juillet 2015

We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We (...)

22 juillet 2015

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

17 juillet 2015

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between (...)

17 juillet 2015

En 1942, le célèbre astronome et physicien belge Georges Lemaître (1894-1966) publie dans le Bulletin de la classe des sciences de l'Académie Royale de Belgique, un article dans lequel il formule une méthode qu'il nomme itération rationnelle. Il redécouvre à la fois le processus du Delta 2 de Aitken et (...)

12 juillet 2015

Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping (...)

11 juillet 2015

We study real rational models of the euclidean affine plane $\mathbbR^2$ up to isomorphisms and up to birational diffeomorphisms. The analogous study in the compact case, that is the classification of real rational models of the real projective plane $\mathbbR\mathbbP^2$ is well known: up to (...)

2 juillet 2015

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give (...)

30 juin 2015

We develop some methods to compute the Makar-Limanov and Derksen invariants, isomorphism classes and automorphism groups for k-domains B, which are constructed from certain Russell k-domains. We propose tools and techniques to distinguish between k-domains with the same Makar-Limanov and (...)

20 juin 2015

The objective of this note is to made preliminary remarks concerning the optimal locomotion of the Copepod swimmer described by a simple model concerning swimming at low Reynolds number, in the framework of Sub-Riemannian geometry. In particular the role of both normal and abnormal geodesics is (...)

20 juin 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

20 juin 2015

We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain (...)

20 juin 2015

Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual (...)

18 juin 2015

We show a simple and easily implementable solution to the word problem for virtual braid groups.

30 mai 2015

En 1902, Robert de Montessus de Ballore démontre la convergence d'une fraction continue algébrique associée à une fonction analytique à l'origine et méromorphe dans un domaine contenant l'origine. Aujourd'hui ce théorème est encore cité. Et le nom Montessus de Ballore sert à nommer des généralisations (...)

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