Equilibrium states for non-uniformly expanding maps: Decay of correlations and strong stability

Castro, A. ; Varandas, P.

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013), p. 225-249 / Harvested from Numdam

Résumé

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.

Détail

Publié le : 2013-01-01

Zbl 1336.37028

DOI : https://doi.org/10.1016/j.anihpc.2012.07.004

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