Preprint A309/2005
Physical measures at the boundary of hyperbolic maps

Ali Tahzibi | Araujo, Vitor

**Keywords: **
Dominated splitting | partial hyperbolicity | physical measures | equilibrium states | random perturbations | stochastic stability

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.