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A pointwise ergodic theorem for Fuchsian groups


We use Series' Markovian coding for words in Fuchsian groups and the Bowen-Series coding of limit sets to prove an ergodic theorem for Cesàro averages of spherical averages in a Fuchsian group.

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[7] A. I. Bufetov Markov averaging and ergodic theorems for several operators. Topology, ergodic theory, real algebraic geometry, 3950, Amer. Math. Soc. Transl. Ser. 2 202 (Amer. Math. Soc., 2001).

[14] A. Nevo Pointwise ergodic theorems for actions of groups. Handbook of dynamical systems. Vol. 1B, 871982 (Elsevier, Amsterdam, 2006).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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