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arXiv · 0803.1943

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

Omri Sarig·Barbara Schapira
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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 $\Z^d$--covers.

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Omri Sarig, Barbara Schapira. 2008-03-13. The generic points for the horocycle flow on a class of hyperbolic surfaces with infinite genus. https://arxiv.org/abs/0803.1943

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