Large deviations and stochastic flows of diffeomorphisms (Q1099483)

Previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold M are extended and then applied to the analysis of the Lyapunov exponents of a stochastic flow of diffeomorphisms of M. An approximation argument relates these results to the behavior near the diagonal \(\Delta\) in M 2 of the associated two-point motion. Finally it is shown, under appropriate non-degeneracy conditions, that the two-point motion is ergodic on M 2-\(\Delta\) if the top Lyapunov exponent is positive.