Genericity of zero Lyapunov exponents

Jairo Bochi

doi:10.1017/S0143385702001165

Genericity of zero Lyapunov exponents

Jairo Bochi

Mathematics

Research output: Contribution to journal › Article › peer-review

149 Scopus citations

Abstract

We show that, for any compact surface, there is a residual (dense G_δ) set of C¹ area-preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé but no proof was available. We also show that for any fixed ergodic dynamical system over a compact space, there is a residual set of continuous SL(2, ℝ)-cocycles which either are uniformly hyperbolic or have zero exponents a.e.

Original language	English (US)
Pages (from-to)	1667-1696
Number of pages	30
Journal	Ergodic Theory and Dynamical Systems
Volume	22
Issue number	6
DOIs	https://doi.org/10.1017/S0143385702001165
State	Published - Dec 2002

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1017/S0143385702001165

Cite this

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Genericity of zero Lyapunov exponents

Abstract

All Science Journal Classification (ASJC) codes

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