Density and Equidistribution of One-Sided Horocycles of a Geometrically Finite Hyperbolic Surface

Details Density and Equidistribution of One-Sided Horocycles of a Geometrically Finite Hyperbolic Surface Density and Equidistribution of One-Sided Horocycles of a Geometrically Finite Hyperbolic Surface

2009-09-22

arxiv.org/abs/0909.3929v1

Mathematics

Dynamical Systems

15 pages

Scientific paper

On geometrically finite negatively curved surfaces, we give necessary and
sufficient conditions for a one-sided horocycle $(h^s u)_{s\ge 0}$ to be dense
in the nonwandering set of the geodesic flow. We prove that all dense one-sided
orbits $(h^su)_{s\ge 0}$ are equidistributed, extending results of [Bu] and
[Scha2] where symmetric horocycles $(h^su)_{s\in\R}$ were considered.

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