Symbolic extensions and partially hyperbolic diffeomorphisms

Lorenzo J. Díaz; Todd Fisher

doi:10.3934/dcds.2011.29.1419

Article Contents

2011, Volume 29, Issue 4: 1419-1441. Doi: 10.3934/dcds.2011.29.1419

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Symbolic extensions and partially hyperbolic diffeomorphisms

Lorenzo J. Díaz^1, and
Todd Fisher^2,

1.
Dep. Matemática PUC-Rio, Marquês de São Vicente 225 22453-900, Rio de Janeiro
2.
Department of Mathematics, Brigham Young University, Provo, UT 84602

Received: October 31, 2009

Revised: July 31, 2010

Published: September 2011

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Abstract

We show there are no symbolic extensions $C^1$-generically among diffeomorphisms containing nonhyperbolic robustly transitive sets with a center indecomposable bundle of dimension at least 2. Similarly, $C^1$-generically homoclinic classes with a center indecomposable bundle of dimension at least 2 that satisfy a technical assumption called index adaptation have no symbolic extensions.

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Mathematics Subject Classification: Primary: 37D30, 37C05, 37C20, 37B10.

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