Bessa, Mário2023-05-252023-05-252007M. Bessa, The Lyapunov exponents of generic zero divergence three-dimensional vector fields, Ergodic Theory and Dynamical Systems, 27(5), 1445-1472 2007http://hdl.handle.net/10400.2/13836We prove that for a C1-generic (dense Gδ) subset of all the conservative vector fields on three-dimensional compact manifolds without singularities, we have for Lebesgue almost every (a.e.) point p ∈ M that either the Lyapunov exponents at p are zero or X is an Anosov vector field. Then we prove that for a C1-dense subset of all the conservative vector fields on three-dimensional compact manifolds, we have for Lebesgue a.e. p ∈ M that either the Lyapunov exponents at p are zero or p belongs to a compact invariant set with dominated splitting for the linear Poincaré flow.engjournal article10.1017/S0143385707000107