Genericity of zero Lyapunov exponents

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Abstract

We show that, for any compact surface, there is a residual (dense Gδ) 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 languageEnglish (US)
Pages (from-to)1667-1696
Number of pages30
JournalErgodic Theory and Dynamical Systems
Volume22
Issue number6
DOIs
StatePublished - Dec 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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