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Please use this identifier to cite or link to this item: http://repositorio.ufba.br/ri/handle/ri/12022

Title: Equilibrium states for non-uniformly expanding maps: Decay of correlations and strong stability
Other Titles: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Authors: Castro, A.
Varandas, Paulo César Rodrigues Pinto
Issue Date: 2013
Publisher: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
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 Hölder 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.
Description: p. 225–249
URI: http://www.repositorio.ufba.br/ri/handle/ri/12022
ISSN: 0294-1449
Appears in Collections:Artigos Publicados em Periódicos (IM)

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