SOME NEGATIVELY CURVED MANIFOLDS WITH CUSPS, MIXING AND COUNTING

Authors
Citation
F. Dalbo et M. Peigne, SOME NEGATIVELY CURVED MANIFOLDS WITH CUSPS, MIXING AND COUNTING, Journal fur die Reine und Angewandte Mathematik, 497, 1998, pp. 141-169
Citations number
33
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00754102
Volume
497
Year of publication
1998
Pages
141 - 169
Database
ISI
SICI code
0075-4102(1998)497:<141:SNCMWC>2.0.ZU;2-#
Abstract
Let X be a Hadamard manifold whose sectional curvature K satisfies -b( 2) less than or equal to K less than or equal to -1. We consider a fam ily of free isometry groups Gamma acting properly discontinuously on X and containing parabolic transformations of divergence type. We show that such groups are of divergent type, we describe the dynamic proper ties of the map T induced by the action of Gamma on the boundary of X and we explore the spectrum of the transfer operator associated with T . As applications, we establish a mixing property for the geodesic flo w on the unit tangent bundle of X/Gamma and we describe the behaviour as a goes to +infinity of the number of primitive closed geodesics on X/Gamma whose length is not larger than a.