Symbolic extensionsfor partially hyperbolic dynamical systems with 2-dimensional center bundle

David Burguet; Todd Fisher

doi:10.3934/dcds.2013.33.2253

Article Contents

2013, Volume 33, Issue 6: 2253-2270. Doi: 10.3934/dcds.2013.33.2253

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Symbolic extensionsfor partially hyperbolic dynamical systems with 2-dimensional center bundle

David Burguet^1, and
Todd Fisher^2,

1.
LPMA Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05
2.
Department of Mathematics, Brigham Young University, Provo, UT 84602

Received: June 30, 2011

Revised: June 30, 2012

Published: June 2013

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Abstract

We relate the symbolic extension entropy of a partially hyperbolic dynamical system to the entropy appearing at small scales in local center manifolds. In particular, we prove the existence of symbolic extensions for $\mathcal{C}^2$ partially hyperbolic diffeomorphisms with a $2$-dimensional center bundle. 200 words.

Keywords:

Symbolic extensions,
partial hyperbolicity.

Mathematics Subject Classification: 37C05, 37C40, 37A35, 37D30, 37B10.

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