Exponentially mixing, locally constant skew extensions of shift maps

Frédéric Naud

Exponentially mixing, locally constant skew extensions of shift maps

Dynamical Systems 2017-01-31 v1

Authors: Frédéric Naud

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- $L^2$ observables. The proof rests on a result of Bourgain-Gamburd and a decoupling argument.

Keywords

exponential mixing locally constant extension skew extension shift map non-abelian extension holder-l2 observable decoupling argument

Cite

@article{arxiv.1701.08659,
  title  = {Exponentially mixing, locally constant skew extensions of shift maps},
  author = {Frédéric Naud},
  journal= {arXiv preprint arXiv:1701.08659},
  year   = {2017}
}

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