DENSITY AND EQUIDISTRIBUTION OF ONE-SIDED HOROCYCLES OF A GEOMETRICALLY FINITE HYPERBOLIC SURFACE

Barbara Schapira (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Mots clés: horospherical point; density; half-horocycles; geometrically finite hyperbolic surfaces; equidistribution; ratio ergodic theorem

Domaines: Systèmes dynamiques [math.DS]

Barbara Schapira. DENSITY AND EQUIDISTRIBUTION OF ONE-SIDED HOROCYCLES OF A GEOMETRICALLY FINITE HYPERBOLIC SURFACE. Journal of the London Mathematical Society, 2011, ⟨10.1112/jlms/jdr012⟩. ⟨hal-00418793⟩