Gioia M. VAGO

1. Gioia M. VAGO - 
    Topological and dynamical classification of the unstable manifolds 
    of one-rectangle systems
    to appear in ``Ergodic Theory & Dynamical Systems''

Abstract - The unstable manifolds of hyperbolic systems admitting a one-rectangle Markov partition are here characterized up to homeomorphism and up to conjugacy of the underlying dynamics in a very easy-to-compute way. We associate to each one-rectangle system a word over the alphabet {+,-}describing the bending of the image rectangle with respect to the initial one. We endow the set {+,-}* of such words with a product  ^  having a dynamical origin. The structure of the non-commutative semigroup ({+,-}*, ^) is completely made explicit. the topological and dynamical properties of the unstable manifolds of one-rectangle systems are translated in terms of the decomposition of the associated words in such a semigroup.

2. Marcy BARGE, James JACKLITCH & Gioia M. VAGO - 
    Homeomorphisms of One-dimensional Inverse Limits with Applications 
    to Substitution Tilings, Unstable Manifolds, and Tent Maps 
    ``Geometry and Topology in Dynamics'', 
    Contemp. Math. 246, Amer. Math. Soc, Providence, RI, 1999

Abstract - Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limit spaces are homeomorphic if and only if the substitutions associated with f and g are weakly equivalent. This, and related results, are applied to one-dimensional substitution tiling spaces, one-dimensional unstable manifolds of hyperbolic sets, and inverse limits of tent maps with periodic critical points.

3. Gioia M. VAGO -
    Variétés instables d'ensembles hyperboliques - 
    Unstable manifolds of hyperbolic sets
    C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) n° 10, 913-918

Résumé - Les variétés instables de systèmes hyperboliques admettant une partition de Markov à un rectangle sont ici caractérisées à homéomorphisme près et à conjugaison topologique (des dynamiques sous-jacentes) près. De telles classes seront décrites à l'aide d'objets algébriques naturellement associés aux systèmes sous-jacents.

Abstract - Here the unstable manifolds of hyperbolic systems admitting a one-rectangle Markov partition are characterised up to homeomorphism and up to topological conjugacy (of the underlying dynamics) in a very easy-to-compute way. The geometrical behaviour of the unstable manifolds is described with the help of an algebraic setting.

4. Gioia M. VAGO - 
    Conjugate unstable manifolds and their underlying geometrized Markov partitions
    Topology and Its Appl, Vol. 104, Issue 1-3 (2000), 255-291

Abstract - Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.

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