Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction

2009/08/31 by José F. Alves, Alves, Jose F., Vilton Pinheiro +1
Mathematics · Physics and Astronomy · #37A25 #37C05 #37C40 #37D25 #37D30 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0908.4570

openalex publication_date 2009/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as T_K M=E^cu⊕ E^s, for which the centre-unstable direction E^cu expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achieve some uniform expanding behavior in the centre-unstable direction. As an application of the main result we obtain certain rates for decay of correlations, large deviations, an almost sure invariance principle and the validity of the Central Limit Theorem.

Citations

• Recurrence times and rates of mixing
• Statistical Properties of Dynamical Systems with Some Hyperbolicity

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