  We prove the following dichotomy for vector fields in a C1-residual subset of
volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents
equal to zero or its orbit has a dominated splitting. As a consequence if we
have a vector field in this residual that cannot be C1-approximated by a vector
field having elliptic periodic orbits, then, there exists a full measure set
such that every orbit of this set admits a dominated splitting for the linear
Poincare flow. 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.
