Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps

Details Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps

2008-03-18

arxiv.org/abs/0803.2654v1

Mathematics

Dynamical Systems

44 pages

Scientific paper

We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms 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.

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