# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

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• ### [hal-01568278] Generalized Johnson homomorphisms for extended N-series

25 juillet, par Kazuo Habiro, Gwénaël Massuyeau
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 (...)
• ### [hal-01226734] Working Examples In Geometric Optimal Control

24 juillet, par Bernard Bonnard, Monique Chyba, Jérémy Rouot
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 (...)
• ### [hal-01542608] Hyperbolicity as an obstruction to smoothability for one-dimensional actions

18 juillet, par Christian Bonatti, Yash Lodha, Michele Triestino
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 (...)
• ### [hal-01178641] Groups with infinitely many ends acting analytically on the circle

17 juillet, par Sébastien Alvarez, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, Carlos Meniño
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 (...)
• ### [hal-01557228] LOCAL BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION IN BIFURCATING MARKOV CHAIN MODEL

13 juillet, par Siméon Valère Bitseki Penda, Angelina Roche
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 (...)

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