Density of half-horocycles on geometrically infinite hyperbolic surfaces

Densité de demi-horocycles sur une surface hyperbolique géométriquement infinie

Barbara Schapira (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Mots clés: horocycles; hyperbolic surface; density; geometrically infinite

Domaines: Systèmes dynamiques [math.DS]

Barbara Schapira. Densité de demi-horocycles sur une surface hyperbolique géométriquement infinie. Ergodic Theory and Dynamical Systems, 2013, 33 (4), pp.1162-1177. ⟨hal-00572881⟩