Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability
arXiv:1205.5358 · doi:10.1016/j.anihpc.2012.07.004
Abstract
We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of Holder continuous observables has a spectral gap and deduce the exponential decay of correlations and the central limit theorem. In particular, we obtain an alternative proof for the existence and uniqueness of the equilibrium states and we prove that the topological pressure varies continuously. Finally, we use the spectral properties of the transfer operators in space of differentiable observables to obtain strong stability results under deterministic and random perturbations.
29 pages, Annales de l'Institut Henri Poincare - Analyse non lineaire (to appear)
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- Equilibrium States for Non-Uniformly Expanding Skew Products
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- Thermodynamic formalism for discontinuous maps and statistical properties of their equilibrium states