CLOSED GEODESICS IN HOMOLOGY CLASSES ON HYPERBOLIC MANIFOLDS WITH CUSPS

Authors
BABILLOT M PEIGNE M
Citation
M. Babillot et M. Peigne, CLOSED GEODESICS IN HOMOLOGY CLASSES ON HYPERBOLIC MANIFOLDS WITH CUSPS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 324(8), 1997, pp. 901-906
Citations number
10
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
324
Issue
8
Year of publication
1997
Pages
901 - 906
Database
ISI
SICI code
0764-4442(1997)324:8<901:CGIHCO>2.0.ZU;2-I
Abstract
On a class of hyperbolic manifolds with infinite volume, we give an as ymptotic estimate for the number of closed geodesics in a given homolo gy class. We show that, in certain cases, the existence of parabolic t ransformations in the fundamental group Gamma of these manifolds has a n effect on this estimate. This happens when the Hausdorff dimension o f the limit set of Gamma is less than 3/2. The geometrical meaning of this critical value remains to be understood.