Bessa, MárioRocha, Jorge2023-05-252023-05-252012M. Bessa, J. Rocha, Contributions to the geometric and ergodic theory of conservative flows. Ergodic Theory and Dynamical Systems, 33(6), 1709-1731, 2013http://hdl.handle.net/10400.2/13837We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue-almost every point, either all of its Lyapunov exponents are equal to zero or its orbit has a dominated splitting. Moreover, we prove that a volume-preserving and C1-stably ergodic flow can be C1-approximated by another volume-preserving flow which is non-uniformly hyperbolic.engjournal article10.1017/etds.2012.110