Physical measures at the boundary of hyperbolic maps

Abstract

We consider diffeomorphisms of a compact manifold with a dominated splitting which is hyperbolic except for a "small" subset of points (Hausdorff dimension smaller than one, e.g. a denumerable subset) and prove the existence of physical measures and their stochastical stability. The physical measures are obtained as zero-noise limits which are shown to satisfy the Entropy Formula.

29 pages, 2 figures, 44 references. Minor corrections

References in corpus (1)

• Stochastic stability at the boundary of expanding maps

Cited by in corpus (1)

• Semicontinuity of entropy, existence of equilibrium states and continuity of physical measures