Physical measures at the boundary of hyperbolic maps

Vítor Araújo; Ali Tahzibi

doi:10.3934/dcds.2008.20.849

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2008, Volume 20, Issue 4: 849-876. Doi: 10.3934/dcds.2008.20.849

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Physical measures at the boundary of hyperbolic maps

Vítor Araújo^1, and
Ali Tahzibi^2,

1.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21.945-970 Rio de Janeiro, RJ
2.
Departamento de Matematica, ICMC-USP São Carlos, Caixa Postal 668, 13560-970 São Carlos-SP

Received: October 31, 2006

Revised: September 30, 2007

Published: September 2008

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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 stochastic stability. The physical measures are obtained as zero-noise limits which are shown to satisfy the Entropy Formula.

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Mathematics Subject Classification: Primary: 37D25. Secondary: 37D30, 37D20.

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