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Working paper

Convergence of spherical averages for actions of Fuchsian Groups

arxiv.org. math. Cornell University, 2018. No. 1805.11743.
Klimenko A. V., Bufetov A. I., Series C.
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.