INFINITESIMAL LYAPUNOV FUNCTIONS, INVARIANT CONE FAMILIES AND STOCHASTIC PROPERTIES OF SMOOTH DYNAMICAL-SYSTEMS

We establish general criteria for ergodicity and Bernoulliness for Bernoulliness for volume-preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C(infinity) Riemannian metric whose geodesic flow is Bernoulli.