2016/01/28 by Armando Castro, ARMANDO CASTRO, Teofilo Nascimento +1 · 11 citations
Engineering · Mathematics · Physics and Astronomy · #Attractor #Central limit theorem #Chaos control and synchronization #Entropy (arrow of time) #Exponential function #Mathematical Dynamics and Fractals #Measure (data warehouse) #Probability distribution #Probability measure #Stability and Controllability of Differential Equations #Topological entropy #Uniqueness #math.DS #msc:37A35 #msc:37C30 #msc:37C40 #msc:37D25 #msc:60F
paper · pdf · doi:10.1017/etds.2015.86
published in Ergodic Theory and Dynamical Systems 37(4), 1060-1101 (Cambridge University Press) · Paper published in Ergodic Theory in Jan. 2016. 45 pages, 2 figures. keywords: Exponential Decay of Correlations,Systems Derived from Anosov, Systems Derived from Solenoid, Thermodynamic Formalism, Partially Hyperbolic Systems, Transfer Operator, Ergodic Theory and Dynamical Systems, published online 28 January 2016
openalex publication_date 2016/01/28 · openalex created_date 2016/06/24 · arxiv created 2016/10/05 · arxiv updated 2016/10/06 · openalex updated_date 2026/08/05
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.