Sur la fonction orbitale des groupes discrets en courbure négative  [ On the orbital function of discrete groups in negative curvature ]
Annales de l'Institut Fourier, Volume 52 (2002) no. 1, p. 145-151
We precise the exponential behavior of the orbital counting function of any discrete isometries group in negative curvature.
Nous précisons le comportement exponentiel de la fonction orbitale d'un quelconque groupe discret d'isométries en courbure négative.
DOI : https://doi.org/10.5802/aif.1880
Classification:  20H10,  37F35
Keywords: discrete groups, hyperbolic geometry, conform densities
@article{AIF_2002__52_1_145_0,
     author = {Roblin, Thomas},
     title = {Sur la fonction orbitale des groupes discrets en courbure n\'egative},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {1},
     year = {2002},
     pages = {145-151},
     doi = {10.5802/aif.1880},
     mrnumber = {1881574},
     zbl = {1008.20040},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2002__52_1_145_0}
}
Roblin, Thomas. Sur la fonction orbitale des groupes discrets en courbure négative. Annales de l'Institut Fourier, Volume 52 (2002) no. 1, pp. 145-151. doi : 10.5802/aif.1880. https://aif.centre-mersenne.org/item/AIF_2002__52_1_145_0/

[B] M. Bourdon Structure conforme au bord et flot géodésique d'un CAT(-1)-espace, L'Ens. Math., Tome 41 (1995), pp. 63-102 | MR 1341941 | Zbl 0871.58069

[GH] E. Ghys; P. De La Harpe Sur les groupes hyperboliques d'après Gromov, Birkhäuser, Prog. in Math., Tome 83 (1990) | MR 1086648 | Zbl 0731.20025

[K] V. Kaimanovich Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds, Ann. Inst. Henri Poincaré, Phys. Theor., Tome 53 (1990) no. 4, pp. 361-393 | Numdam | MR 1096098 | Zbl 0725.58026

[Man] A. Manning Topological entropy for geodesic flows, Ann. Math., Tome 110 (1979), pp. 567-573 | Article | MR 554385 | Zbl 0426.58016

[Mar] G.A. Margulis Applications of ergodic theory to the investigation of manifolds of negative curvature, Funct. Anal. Appl., Tome 3 (1969), p. 335-336 | Article | MR 257933 | Zbl 0207.20305

[N] P.J. Nicholls The ergodic theory of discrete groups, Cambridge University Press (1989) | MR 1041575 | Zbl 0674.58001

[Pa] S.J. Patterson The limit set of a Fuchsian group, Acta Math., Tome 136 (1976), pp. 241-273 | Article | MR 450547 | Zbl 0336.30005

[PoSh] M. Pollicott; R. Sharp Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature, Invent. Math., Tome 117 (1994), pp. 275-302 | Article | MR 1273266 | Zbl 0804.58009

[R] T. Roblin Sur la théorie ergodique des groupes discrets en géométrie hyperbolique (1999) (Thèse de doctorat de l'Université de Paris-Sud)

[Su1] D. Sullivan The density at infinity of a discrete group of hyperbolic motions, Publ. Math. I.H.E.S., Tome 50 (1979), pp. 171-202 | Numdam | MR 556586 | Zbl 0439.30034

[Su2] D. Sullivan Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math., Tome 153 (1984), pp. 259-277 | Article | MR 766265 | Zbl 0566.58022