Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot; Marc Peigné

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 1, page 119-163
  • ISSN: 0037-9484

Abstract

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We consider a large class of non compact hyperbolic manifolds M = ℍ n / Γ with cusps and we prove that the winding process ( Y t ) generated by a closed 1 -form supported on a neighborhood of a cusp 𝒞 , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp 𝒞 and the Poincaré exponent δ of Γ . No assumption on the value of δ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.

How to cite

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Babillot, Martine, and Peigné, Marc. "Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps." Bulletin de la Société Mathématique de France 134.1 (2006): 119-163. <http://eudml.org/doc/272432>.

@article{Babillot2006,
abstract = {We consider a large class of non compact hyperbolic manifolds $M= \mathbb \{H\} ^n/\Gamma $ with cusps and we prove that the winding process $(Y_t)$ generated by a closed $1$-form supported on a neighborhood of a cusp $\mathcal \{C\} $, satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp $\mathcal \{C\} $ and the Poincaré exponent $\delta $ of $\Gamma $. No assumption on the value of $\delta $ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.},
author = {Babillot, Martine, Peigné, Marc},
journal = {Bulletin de la Société Mathématique de France},
keywords = {geodesic flow; asymptotic winding; hyperbolic manifolds; central limit theorem; stable law; transfer operator},
language = {eng},
number = {1},
pages = {119-163},
publisher = {Société mathématique de France},
title = {Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps},
url = {http://eudml.org/doc/272432},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Babillot, Martine
AU - Peigné, Marc
TI - Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 1
SP - 119
EP - 163
AB - We consider a large class of non compact hyperbolic manifolds $M= \mathbb {H} ^n/\Gamma $ with cusps and we prove that the winding process $(Y_t)$ generated by a closed $1$-form supported on a neighborhood of a cusp $\mathcal {C} $, satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp $\mathcal {C} $ and the Poincaré exponent $\delta $ of $\Gamma $. No assumption on the value of $\delta $ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.
LA - eng
KW - geodesic flow; asymptotic winding; hyperbolic manifolds; central limit theorem; stable law; transfer operator
UR - http://eudml.org/doc/272432
ER -

References

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