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1 December 2011 New criteria for ergodicity and nonuniform hyperbolicity
F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Tahzibi, R. Ures
Duke Math. J. 160(3): 599-629 (1 December 2011). DOI: 10.1215/00127094-1444314

Abstract

In this work we obtain a new criterion to establish ergodicity and nonuniform hyperbolicity of smooth measures of diffeomorphisms of closed connected Riemannian manifolds. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of nonzero Lyapunov exponents in some contexts.

In the partial hyperbolicity context, we obtain that stably ergodic diffeomorphisms are C1-dense among volume-preserving partially hyperbolic diffeomorphisms with 2-dimensional center bundle. This is motivated by a well-known conjecture of Pugh and Shub.

Citation

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F. Rodriguez Hertz. M. A. Rodriguez Hertz. A. Tahzibi. R. Ures. "New criteria for ergodicity and nonuniform hyperbolicity." Duke Math. J. 160 (3) 599 - 629, 1 December 2011. https://doi.org/10.1215/00127094-1444314

Information

Published: 1 December 2011
First available in Project Euclid: 7 November 2011

zbMATH: 1290.37011
MathSciNet: MR2852370
Digital Object Identifier: 10.1215/00127094-1444314

Subjects:
Primary: 37D25
Secondary: 37D30, 37D35

Rights: Copyright © 2011 Duke University Press

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Vol.160 • No. 3 • 1 December 2011
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