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Physical measures at the boundary of hyperbolic maps

Vitor Araujo·Ali Tahzibi
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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.

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Vitor Araujo, Ali Tahzibi. 2007-07-15. Physical measures at the boundary of hyperbolic maps. https://arxiv.org/abs/math/0409391

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