Exponentially mixing, locally constant skew extensions of shift maps

2017/01/30 by Frédéric Naud, Naud, Frédéric
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1701.08659

openalex publication_date 2017/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that locally constant toral extensions of hyperbolic systems can never mix at an exponential rate. In this note we exhibit some examples of non-abelian locally constant compact extensions of the shift map which are exponentially mixing for Holder-L² observables. The proof rests on a result of Bourgain-Gamburd and a decoupling argument.

Citations

• On mixing properties of compact group extensions of hyperbolic systems

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