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

Soient X un espace symétrique de type non compact et Γ 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 Γ sur X.

Let X be a symmetric space of noncompact type and Γ 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 Γ on X.

DOI : 10.5802/aif.2102
Classification : 22E40, 53C35, 37D35
Mot clés : groupes de Lie, sous-groupes discrets, géométrie en rang supérieur, formalisme thermodynamique.
Keywords: Lie groups, discrete subgroups, higher rank geometry, thermodynamical formalism
Quint, Jean-François 1

1 Université Paris VII Denis Diderot, Institut de mathématique de Jussieu, case 7012, 2 place Jussieu, 75251 Paris cedex 05 (France)
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Quint, Jean-François. Groupes de Schottky et comptage. Annales de l'Institut Fourier, Tome 55 (2005) no. 2, pp. 373-429. doi : 10.5802/aif.2102. https://aif.centre-mersenne.org/articles/10.5802/aif.2102/

[16 J.-F. Quint Mesures de Patterson-Sullivan en rang supérieur, Geometric and functional analysis, Volume 12 (2002), pp. 776-809 | DOI | MR | Zbl

[1] N. Anantharaman Precise counting results for closed orbits of Anosov flows, Annales Scientifiques de l'École Normale Supérieure, Volume 33 (2000), pp. 33-56 | Numdam | MR | Zbl

[2] M. Babillot; F. Ledrappier Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic theory and dynamical systems, Volume 18 (1998), pp. 17-39 | MR | Zbl

[3] Y. Benoist Propriétés asymptotiques des groupes linéaires, Geometric and functional analysis, Volume 7 (1997), pp. 1-47 | DOI | MR | Zbl

[4] Y. Benoist Propriétés asymptotiques des groupes linéaires (II), Advanced studies in pure mathematics, Volume 26 (2000), pp. 33-48 | MR | Zbl

[5] J.-P. Conze; Y. Guivarc'h Limit sets of groups of linear transformations (Sankhya Series A), Volume 62 (2000), pp. 367-385 | Zbl

[6] D. Dolgopyat Prevalence of rapid mixing in hyperbolic flows, Ergodic theory and dynamical systems, Volume 18 (1998), pp. 1097-1114 | DOI | MR | Zbl

[7] A. Eskin; C. McMullen Mixing, counting and equidistribution in Lie groups, Duke mathematical journal, Volume 71 (1993), pp. 181-209 | DOI | MR | Zbl

[8] S. Helgason Differential geometry, Lie groups and symmetric spaces, Pure and Applied Mathematics, 80, Academic Press, San Diego, 1978 | MR | Zbl

[9] A. Katsuda; T. Sunada Closed orbits in homology classes, Publications mathématiques de l'IHES, Volume 71 (1990), pp. 5-32 | Numdam | MR | Zbl

[10] S. P. Lalley Renewal theorems in symbolic dynamics, with application to geodesic flows, noneuclidean tessellations and their fractal limits, Acta mathematica, Volume 163 (1989), pp. 1-55 | DOI | MR | Zbl

[11] G. Prasad -regular elements in Zariski dense subgroups, Oxford quaterly journal of mathematics, Volume 45 (1994), pp. 541-545 | MR | Zbl

[12] W. Parry; M. Pollicott Zeta functions and the periodic orbit structure for hyperbolic dynamics (Astérisque) (1990), pp. 187-188 | Zbl

[13] M. Pollicott; R. Sharp Linear actions of free groups, Annales de l'institut Fourier, Volume 51 (2001), pp. 131-150 | DOI | Numdam | MR | Zbl

[14] M. Pollicott; R. Sharp Asymptotic expansions for closed orbits in homology classes, GeometriæDedicata, Volume 87 (2001), pp. 123-160 | MR | Zbl

[15] J.-F. Quint Divergence exponentielle des sous-groupes discrets en rang supérieur, Commentarii Mathematicii Helvetici, Volume 77 (2002), pp. 563-608 | DOI | MR | Zbl

[17] J.-F. Quint L'indicateur de croissance des groupes de Schottky, Ergodic theory and dynamical systems, Volume 23 (2003), pp. 249-272 | MR | Zbl

[18] Th. Roblin Ergodicité et équidistribution en courbure négative (Mémoires), Volume 95 (2003) | Numdam | Zbl

[18] C. Series The infinite word problem and limit sets in Fuchsian groups, Ergodic theory and dynamical systems, Volume 1 (1981), pp. 337-360 | MR | Zbl

[19] J. Tits Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque, Journal f\" ur die reine und angewandte Mathematik, Volume 247 (1971), pp. 196-220 | MR | Zbl

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