English

The generic points for the horocycle flow on a class of hyperbolic surfaces with infinite genus

Dynamical Systems 2008-12-18 v1

Abstract

A point is called generic for a flow preserving an infinite ergodic invariant Radon measure, if its orbit satisfies the conclusion of the ratio ergodic theorem for every pair of continuous functions with compact support and non-zero integrals. The generic points for horocycle flows on hyperbolic surfaces of finite genus are understood, but there are no results in infinite genus. We give such a result, by characterizing the generic points for Zd\Z^d--covers.

Keywords

Cite

@article{arxiv.0803.1943,
  title  = {The generic points for the horocycle flow on a class of hyperbolic surfaces with infinite genus},
  author = {Omri Sarig and Barbara Schapira},
  journal= {arXiv preprint arXiv:0803.1943},
  year   = {2008}
}