Preprint A04/2001
Genericity of zero Lyapunov exponents

Jairo Bochi

**Keywords: **
Lyapunov Exponents | Anosov diffeomorphisms | area-preserving diffeomorphisms

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. Ma\~{n}\'{e}, 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 $\sl2r$-cocycles which either are uniformly
hyperbolic or have zero exponents a.e.