Horocycle flows on surfaces with infinite genus: Geometric and ergodic aspects of group actions

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Abstract

We study the ergodic theory of horocycle flows on hyperbolic surfaces with infinite genus. In this case, the nontrivial ergodic invariant Radon measures are all infinite. We explain the relation between these measures and the positive eigenfunctions of the Laplacian on the surface. In the special case of Zd-covers of compact hyperbolic surfaces, we also describe some of their ergodic properties, paying special attention to equidistribution and to generalized laws of large numbers.

Original languageEnglish
Title of host publicationGeometric and Ergodic Aspects of Group Actions
EditorsS. G. Dani, Anish Ghosh
PublisherSpringer Verlag
Chapter2
Pages21-81
Number of pages61
ISBN (Electronic)978-981-15-0683-3
ISBN (Print)978-981-15-0682-6
DOIs
StatePublished - 14 Jan 2020

Publication series

NameInfosys Science Foundation Series in Mathematical Sciences
ISSN (Print)2364-4036

All Science Journal Classification (ASJC) codes

  • General Mathematics

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