On the orbital function of discrete groups in negative curvature

Thomas Roblin[1]

  • [1] Université de Paris VI, Laboratoire de Probabilités et Modèles Aléatoires (UMR 7599), Boî te Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05 (France)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 1, page 145-151
  • ISSN: 0373-0956

Abstract

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We precise the exponential behavior of the orbital counting function of any discrete isometries group in negative curvature.

How to cite

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Roblin, Thomas. "Sur la fonction orbitale des groupes discrets en courbure négative." Annales de l’institut Fourier 52.1 (2002): 145-151. <http://eudml.org/doc/115970>.

@article{Roblin2002,
abstract = {Nous précisons le comportement exponentiel de la fonction orbitale d'un quelconque groupe discret d'isométries en courbure négative.},
affiliation = {Université de Paris VI, Laboratoire de Probabilités et Modèles Aléatoires (UMR 7599), Boî te Courrier 188, 4 place Jussieu, 75252 Paris Cedex 05 (France)},
author = {Roblin, Thomas},
journal = {Annales de l’institut Fourier},
keywords = {discrete groups; hyperbolic geometry; conform densities},
language = {fre},
number = {1},
pages = {145-151},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la fonction orbitale des groupes discrets en courbure négative},
url = {http://eudml.org/doc/115970},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Roblin, Thomas
TI - Sur la fonction orbitale des groupes discrets en courbure négative
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 1
SP - 145
EP - 151
AB - Nous précisons le comportement exponentiel de la fonction orbitale d'un quelconque groupe discret d'isométries en courbure négative.
LA - fre
KW - discrete groups; hyperbolic geometry; conform densities
UR - http://eudml.org/doc/115970
ER -

References

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  7. S.J. Patterson, The limit set of a Fuchsian group, Acta Math. 136 (1976), 241-273 Zbl0336.30005MR450547
  8. M. Pollicott, R. Sharp, Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature, Invent. Math. 117 (1994), 275-302 Zbl0804.58009MR1273266
  9. T. Roblin, Sur la théorie ergodique des groupes discrets en géométrie hyperbolique, (1999) 
  10. D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Publ. Math. I.H.E.S. 50 (1979), 171-202 Zbl0439.30034MR556586
  11. D. Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), 259-277 Zbl0566.58022MR766265

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