Preprint A309/2004
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.