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

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

2008-03-13

arxiv.org/abs/0803.1943v1

Mathematics

Dynamical Systems

Scientific paper

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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