Statistical properties of the maximal entropy measure for partially hyperbolic attractors. (28th January 2016)

• Record Type: Journal Article
• Authors: CASTRO, ARMANDO; NASCIMENTO, TEÓFILO
• Is Part Of: Ergodic theory and dynamical systems. Volume 37:Number 4(2017)
• Page Start: 1060
• Page End: 1101
• Publication Date: 2016-01-28
• Subjects: Ergodic theory -- Periodicals; Differentiable dynamical systems -- Periodicals; 515.42
• DOI: 10.1017/etds.2015.86
• Languages: English
• ISSNs: 0143-3857

Abstract

Abstract : We show the existence and uniqueness of the maximal entropy probability measure for partially hyperbolic diffeomorphisms which are semiconjugate to non-uniformly expanding maps. Using the theory of projective metrics on cones, we then prove exponential decay of correlations for Hölder continuous observables and the central limit theorem for the maximal entropy probability measure. Moreover, for systems derived from a solenoid, we also prove the statistical stability for the maximal entropy probability measure. Finally, we use such techniques to obtain similar results in a context containing partially hyperbolic systems derived from Anosov.