Statistical Properties of Maximal Entropy Measure for partially hyperbolic attractors
Augusto Armando de Castro Junior | Antônio Teófilo Ataide Nascimento
Thermodynamical Formalism ; Maximal Entropy Measure; Partially Hyperbolic Attractors; Transfer Operators
We show the existence and uniqueness of the maximal entropy probability measure for partially hyperbolic diffeomorphisms which are semi-conjugate to nonuniformly expanding maps. And especially, we obtain good statistical properties for such measures. More precisely, using the theory of projective metric on cones we prove exponential decay of correlations for H\"older continuous observables and the central limit theorem for the maximal entropy probability measure. Furthermore, for systems derived from solenoid-like we also prove the statistical stability for the maximal entropy probability measure that we constructed.