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## Densit\'e de demi-horocycles sur une surface hyperbolique g\'eom\'etriquement infinie

### Abstract

On the unit tangent bundle of a hyperbolic surface, we study the density of positive orbits $(h^s v)_{s\ge 0}$ under the horocyclic flow. More precisely, given a full orbit $(h^sv)_{s\in \R}$, we prove that under a weak assumption on the vector $v$, both half-orbits $(h^sv)_{s\ge 0}$ and $(h^s v)_{s\le 0}$ are simultaneously dense or not in the nonwandering set $\mathcal{E}$ of the horocyclic flow. We give also a counter-example to this result when this assumption is not satisfied.Comment: 13 pages, 6 figure

Topics: Mathematics - Dynamical Systems
Year: 2011
OAI identifier: oai:arXiv.org:1103.0443