$\mathcal{C}^2$ surface diffeomorphisms have symbolic extensions
Dynamical Systems
2010-03-02 v2
Abstract
We prove that surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. Following the strategy of T.Downarowicz and A.Maass \cite{Dow} 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.
Cite
@article{arxiv.0912.2018,
title = {$\mathcal{C}^2$ surface diffeomorphisms have symbolic extensions},
author = {David Burguet},
journal= {arXiv preprint arXiv:0912.2018},
year = {2010}
}