Abstract
Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show 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 these averages are given by a finite number of physical absolutely continuous stationary probability measures.We use this result to deduce that situations with infinitely many sinks and Hénon-like attractors are not stable under random perturbations, e.g., Newhouse’s and Colli’s phenomena in the generic unfolding of a quadratic homoclinic tangency by a one-parameter family of diffeomorphisms.
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