| Résume | We prove ergodicity of conservative random dynamics satisfying a certain hyperbolicity condition. The new feature of our result is that we do not require the non-existence of zero Lyapunov exponents. As a particular application, we show that if R_1, R_2 in SO(d + 1), d ≥ 2, generate a dense subgroup, then any pair (f_1, f_2) of infinitely smooth volume preserving diffeomorphisms of the d-dimensional sphere that is sufficiently close to (R_1, R_2) is ergodic with respect to the volume. Previously this was only known to hold when d is even by a result of Dolgopyat and Krikorian. Joint work in progress with Jonathan DeWitt and Dmitry Dolgopyat. |
