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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	191-236
Number of pages	46
Journal	Inventiones Mathematicae
Volume	186
Issue number	1
DOIs	https://doi.org/10.1007/s00222-011-0317-8
Publication status	Published - 1 Oct 2011
Externally published	Yes

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C2 surface diffeomorphisms have symbolic extensions

Abstract

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C² surface diffeomorphisms have symbolic extensions