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Pré-Publication, Document De Travail Année : 2019

Convergence of spherical averages for actions of Fuchsian Groups

Résumé

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.

Dates et versions

hal-02110628 , version 1 (25-04-2019)

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Alexander I. Bufetov, Alexey Klimenko, Caroline Series. Convergence of spherical averages for actions of Fuchsian Groups. 2019. ⟨hal-02110628⟩
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