Preprint D93/2011
EQUILIBRIUM STATES FOR NON-UNIFORMLY EXPANDING MAPS: DECAY OF CORRELATIONS AND STRONG STABILITY
Paulo Varandas | Castro JĂșnior, Armando
Keywords: Equilibrium states | Non-uniformly expanding maps | Projective metrics | Cones
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 Hólder 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.