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Annales scientifiques de l'ENS - Titles - série 4, 51 (2018)

Titles < série 4, 51

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 51, fascicule 1 (2018)

Yuri Lima, Carlos Matheus
Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities
Annales scientifiques de l'ENS 51, fascicule 1 (2018), 1-38

Télécharger cet article : Fichier PDF

Résumé :
Dynamique symbolique pour les systèmes non-uniformément hyperboliques avec discontinuités
Nous construisons une dynamique symbolique pour les applications non uniformément hyperboliques d'une surface ayant un ensemble de discontinuités D. La dérivée de l'application peut ne pas être bornée, de l'ordre d'une puissance négative de la distance à D. Sous certaines conditions géométriques naturelles sur l'espace des phases M, nous codifions un ensemble d'orbites non uniformément hyperboliques qui ne s'approchent pas exponentiellement vite de D. Notre résultat s'applique aux billards planaires non uniformément hyperboliques tels que les billards de Bunimovich.

Mots-clefs : Billards, Partition de Markov, dynamique symbolique.

Abstract:
This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities D. We allow the derivative of points nearby D to be unbounded, of the order of a negative power of the distance to D. Under natural geometrical assumptions on the underlying space M, we code a set of non-uniformly hyperbolic orbits that do not converge exponentially fast to D. The results apply to non-uniformly hyperbolic planar billiards, e.g., Bunimovich billiards.

Keywords: Billiards, Markov partition, symbolic dynamics.

Class. math. : 37B10, 37D25, 37D50; 37C35.


ISSN : 0012-9593
DOI : 10.24033/asens.2350
Publié avec le concours de : Centre National de la Recherche Scientifique

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