Article Contents
Article Contents

# Physical measures at the boundary of hyperbolic maps

• 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 stochastic stability. The physical measures are obtained as zero-noise limits which are shown to satisfy the Entropy Formula.
Mathematics Subject Classification: Primary: 37D25. Secondary: 37D30, 37D20.

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