Young structures for partially hyperbolic systems with mostly contracting central direction

2025/03/27 by José F. Alves, Alves, José F., João S. Matias +1
Engineering · Mathematics · Physics and Astronomy · #37A05 #37A25 #37D25 #37D30 #60F05 #60F10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2503.21429

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We establish the existence of Young structures for a broad class of partially hyperbolic diffeomorphisms with a splitting TM = E^cs ⊕ E^uu, under exactly the same conditions that ensure the existence of SRB measures in a previous work by Bonatti and Viana. This extends the applicability of statistical techniques to systems where statistical properties remained largely unexplored. Our approach refines previous methods, introducing key adaptations to the partially hyperbolic setting. These results provide a foundation for obtaining decay of correlations, Central Limit Theorem, large deviations and a vector-valued almost sure invariance principle in this class of dynamical systems.

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