Inventiones mathematicae

, Volume 186, Issue 1, pp 191–236

\(\mathcal{C}^{2}\) surface diffeomorphisms have symbolic extensions


DOI: 10.1007/s00222-011-0317-8

Cite this article as:
Burguet, D. Invent. math. (2011) 186: 191. doi:10.1007/s00222-011-0317-8


We prove that \(\mathcal{C}^{2}\) 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.

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.CMLA-ENS CachanCachan CedexFrance

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