Existence and stability of equilibrium states for robust classes of non-uniformly hyperbolic maps
Equilibrium states | non-uniform hyperbolicity | statistical and stochastic stability
We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local diffeomorphisms on compact manifolds and Holder continuous potentials with not very large oscillation. No Markov structure is assumed. If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property. Under mild additional assumptions we also prove that the equilibrium states vary continuously with the dynamics and the potentials (statistical stability) and are also stable under stochastic perturbations of the transformation.