IMPA

Preprint serie C 48/2006

The Lyapunov exponents of conservative continuous-time dynamical systems

Mário Bessa

Keywords:
Lyapunov exponents, dominated splitting, volume-preserving flows.

Abstract:
We prove that for a C1-generic subset of all the conservative vector fields on 3-dimensional compact manifolds without singularities, we have for Lebesgue a.e. point p that either the Lyapunov exponents at p are zero or the vector field is an Anosov vector field. We also prove a similar version of the previous result in the setting of conservative non-autonomous linear differential systems in the C0-topology. Finally we prove that for a C1-dense subset of all the conservative vector fields on 3-dimensional compact manifolds with singularities, we have for Lebesgue a.e. point that either the Lyapunov exponents at p are zero or p belongs to a compact invariant set with dominated splitting for the linear Poincare flow.

MSC 2000:
37-02    Research exposition (monographs, survey articles)


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