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arXiv · 0909.3929

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

Barbara Schapira
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Abstract

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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Barbara Schapira. 2009-09-22. Density and Equidistribution of One-Sided Horocycles of a Geometrically Finite Hyperbolic Surface. https://doi.org/10.1112/jlms%2Fjdr012

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