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arXiv · 1805.11743

Convergence of spherical averages for actions of Fuchsian Groups

Alexander I. Bufetov·Alexey Klimenko·Caroline Series
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Abstract

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving a reversible Markov chain to which methods previously introduced by the first author for the case of free groups may be applied.

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Alexander I. Bufetov, Alexey Klimenko, Caroline Series. 2018-05-29. Convergence of spherical averages for actions of Fuchsian Groups. https://arxiv.org/abs/1805.11743

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