Preprint C48/2006
The Lyapunov exponents of conservative continuous-time dynamical systems
Mário Bessa
Keywords: Lyapunov Exponents | Dominated splitting | volume-preserving flows.
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.