A symmetric Markov coding and the ergodic theorem for actions of Fuchsian groups. (English) Zbl 1511.20201
Summary: The main result of this note is the pointwise convergence of spherical averages for measure-preserving actions of Fuchsian groups. The proof relies on a new self-inverse Markovian symbolic coding for Fuchsian groups and the method of Markov operators.
MSC:
| 20H10 | Fuchsian groups and their generalizations (group-theoretic aspects) |
| 22D40 | Ergodic theory on groups |
| 30F35 | Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
References:
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