Groupes de Schottky et comptage

Quint, Jean-François

Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 373-429.

Soient $X$ un espace symétrique de type non compact et $\Gamma$ un groupe discret d’isométries de $X$ du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de $\Gamma$ sur $X$.

Let $X$ be a symmetric space of noncompact type and $\Gamma$ a discrete group of isometries of $X$ of Schottky type. In this paper, we give asymptotics of the orbitals counting functions associated to the action of $\Gamma$ on $X$.

Classification : 22E40, 53C35, 37D35
Mots-clés : groupes de Lie, sous-groupes discrets, géométrie en rang supérieur, formalisme thermodynamique.
Keywords: Lie groups, discrete subgroups, higher rank geometry, thermodynamical formalism

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