Preprint D122/2015
Statistical Properties of Maximal Entropy Measure for partially hyperbolic attractors

Augusto Armando de Castro Junior | Antônio Teófilo Ataide Nascimento

**Keywords: **
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.