  We obtain some results of existence and continuity of physical measures
through equilibrium states and apply these to non-uniformly expanding
transformations on compact manifolds with non-flat critical sets, obtaining
sufficient conditions for continuity of physical measures and, for local
diffeomorphisms, necessary and sufficient conditions for stochastic stability.
In particular we show that, under certain conditions, stochastically robust
non-uniform expansion implies existence and continuous variation of physical
measures.
