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Genericity of zero Lyapunov exponents

Published online by Cambridge University Press:  06 November 2002

JAIRO BOCHI
Affiliation:
IMPA, Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil (e-mail: bochi@impa.br)

Abstract

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.

Type
Research Article
Copyright
2002 Cambridge University Press

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