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Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability
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.Comment: 29 pages, Annales de l'Institut Henri Poincare - Analyse non lineaire
(to appear
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