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  • Ergodic Theory and Dynamical Systems, Volume 22, Issue 6
  • December 2002, pp. 1667-1696

Genericity of zero Lyapunov exponents

  • JAIRO BOCHI (a1)
  • DOI:
  • Published online: 01 November 2002

We show that, for any compact surface, there is a residual (dense G_{\delta}) set of C^{1} 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,\mathbb{R})-cocycles which either are uniformly hyperbolic or have zero exponents a.e.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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