The local $C^1$-density of stable ergodicity

Yunhua Zhou

doi:10.3934/dcds.2013.33.2621

Article Contents

2013, Volume 33, Issue 7: 2621-2629. Doi: 10.3934/dcds.2013.33.2621

This issue Previous Article Next Article Stability of nonautonomous equations and Lyapunov functions

The local $C^1$-density of stable ergodicity

Yunhua Zhou^1,

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331

Received: May 31, 2012

Revised: October 31, 2012

Published: June 2013

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Abstract

In this paper, we prove that stable ergodicity is $C^1$-dense among conservative partially hyperbolic systems which, in a stable way, have two ergodic measures such that one has all center Lyapunov exponents non-negative and the other one has all center Lyapunov exponents non-positive.

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Mathematics Subject Classification: Primary: 37D30, 37C40; Secondary: 37A25.

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