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Statistical properties of the maximal entropy measure for partially hyperbolic attractors

Published online by Cambridge University Press:  28 January 2016

ARMANDO CASTRO  and
TEÓFILO NASCIMENTO
ARMANDO CASTRO
Affiliation:
Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110, Salvador-Ba, Brazil email armando@impa.br
TEÓFILO NASCIMENTO
Affiliation:
Departamento de Ciências Exatas e da Terra – Campus II, Universidade do Estado da Bahia, Br 110, km 03, 48.040-210, Alagoinhas-Ba, Brazil email atnascimento@uneb.br
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 4 , June 2017 , pp. 1060 - 1101
Copyright
© Cambridge University Press, 2016 

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