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

David Burguet (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

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 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.

Domaines: Systèmes dynamiques [math.DS]

David Burguet. $\mathcal{C}^2$ surface diffeomorphisms have symbolic extensions. 2010. ⟨hal-00440412v3⟩