Equilibrium states for a class of skew-products

2018/08/06 by Maria Carvalho, Carvalho, Maria, Sebastián A. Pérez +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1808.01970

openalex publication_date 2018/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider skew-products on M× \mathbbT², where M is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. This class of dynamics includes the open sets of Ω-non-stable systems introduced by Abraham, Smale and Shub. We present sufficient conditions, both on the skew-products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability.

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