Affordable Access

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

Authors
  • Burguet, David
Type
Preprint
Publication Date
Mar 02, 2010
Submission Date
Dec 10, 2009
Source
arXiv
License
Yellow
External links

Abstract

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.

Report this publication

Statistics

Seen <100 times