C2 surface diffeomorphisms have symbolic extensions

David Burguet

doi:10.1007/s00222-011-0317-8

C² surface diffeomorphisms have symbolic extensions

David Burguet

ENS Paris-Saclay

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

18 Citations (Scopus)

Résumé

We prove that C² surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass (Invent. Math. 176:617-636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls by contracting maps in a approach combining hyperbolic theory and Yomdin's theory.

langue originale	Anglais
Pages (de - à)	191-236
Nombre de pages	46
journal	Inventiones Mathematicae
Volume	186
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00222-011-0317-8
état	Publié - 1 oct. 2011
Modification externe	Oui

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10.1007/s00222-011-0317-8

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AB - We prove that C2 surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of Downarowicz and Maass (Invent. Math. 176:617-636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls by contracting maps in a approach combining hyperbolic theory and Yomdin's theory.

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C2 surface diffeomorphisms have symbolic extensions

Résumé

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C² surface diffeomorphisms have symbolic extensions