2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161510We 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.29 pages, 2 figures, 44 references. Minor correctionsDynamical Systems37D25; 37D30; 37D20text