New criteria for ergodicity and nonuniform hyperbolicity

F. Rodriguez Hertz, M. A. Rodriguez Hertz, A. Tahzibi, R. Ures

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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 C 1-dense among volume-preserving partially hyperbolic diffeomorphisms with 2-dimensional center bundle. This is motivated by a well-known conjecture of Pugh and Shub.

Original languageEnglish (US)
Pages (from-to)599-629
Number of pages31
JournalDuke Mathematical Journal
Volume160
Issue number3
DOIs
StatePublished - Dec 1 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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