Attractors and time averages for random maps

Considering random noise in finite dimensional parameterized families of di ffeomorphisms of a compact finite dimensional boundaryless manifold M, we s how the existence of time averages for almost every orbit of each point of M, imposing mild conditions on the families; see Section 2.4. Moreover thes e averages are given by a finite number of physical absolutely continuous s tationary probability measures. We use this result to deduce that situations with infinitely many sinks and Henon-like attractors are not stable under random perturbations, e.g., New house's and Colli's phenomena in the generic unfolding of a quadratic homoc linic tangency by a one-parameter family of diffeomorphisms. (C) 2000 Editi ons scientifiques et medicales Elsevier SAS.