Densité de demi-horocycles sur une surface hyperbolique géométriquement infinie

Details Densité de demi-horocycles sur une surface hyperbolique géométriquement infinie Densité de demi-horocycles sur une surface hyperbolique géométriquement infinie

2011-03-02

arxiv.org/abs/1103.0443v1

Mathematics

Dynamical Systems

13 pages, 6 figures

Scientific paper

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.

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