Symbolic extensions for nonuniformly entropy expanding maps

Volume 121 / 2010

David Burguet Colloquium Mathematicum 121 (2010), 129-151 MSC: 37C40, 37A35. DOI: 10.4064/cm121-1-12

Abstract

A nonuniformly entropy expanding map is any $\mathcal{C}^1$ map defined on a compact manifold whose ergodic measures with positive entropy have only nonnegative Lyapunov exponents. We prove that a $\mathcal{C}^r$ nonuniformly entropy expanding map $T$ with $r>1$ has a symbolic extension and we give an explicit upper bound of the symbolic extension entropy in terms of the positive Lyapunov exponents by following the approach of T. Downarowicz and A. Maass [Invent. Math. 176 (2009)].

Authors

  • David BurguetCMLA-ENS Cachan
    61 avenue du président Wilson
    94235 Cachan Cedex, France
    e-mail

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