In this talk we will present some recent contribution to the thermodynamic formalism for partially hyperbolic attractors of non-singular endomorphisms. These attractors admit an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. We prove these attractors have finitely many SRB measures, that these are hyperbolic, and that the SRB measure is unique provided the dynamics is transitive.  Moreover, these SRB measures are statistically stable (in the weak$^*$ topology) and the entropy of the SRB measure varies continuously with respect to the endomorphism. These results hold for attractors of Axiom A endomorphisms and robust classes of partially hyperbolic endomorphisms derived from Anosov endomorphisms.

This is a joint work with Anderson Cruz (Brazil).

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