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Masseye Gaye; Cheikh Lo
Sur l’inexistence d’ensembles minimaux pour le flot horocyclique
(On the non-existence of minimal sets for the horocycle flow)
Confluentes Mathematici, 9 no. 1 (2017), p. 95-104, doi: 10.5802/cml.37
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Class. Math.: 37D40, 20H10, 14H55, 30F35
Keywords: surface hyperbolique, ensemble minimal, orbite horocyclique, point limite.

Résumé - Abstract

The topological dynamics of the horocycle flow $h_\mathbb{R}$ on the unitary tangent bundle of a geometrically finite surface $S$ is well known. In particular in this case a $h_\mathbb{R}$-minimal set exists always. When the surface is geometrically infinite, the behaviour of this flow depends on the action of the fundamental group $\pi _1(S)$ of the surface on the boundary of the hyperbolic plane. The aim of this paper is to give a non-existence condition of $h_\mathbb{R}$-minimal sets and use it to construct a family of geometrically infinite surfaces on which the horocyclic flow has no minimal sets.

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