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Precise counting results for closed orbits of Anosov flows
 

Summary: Precise counting results for closed
orbits of Anosov flows
Nalini Anantharaman
Laboratoire de Probabilit’es (UMR 7599, CNRS)
Universit’e Paris 6
4, Place Jussieu
75252 Paris Cedex 05, France
ABSTRACT : We study the problem of counting closed geodesics according to their
lengths and under homological constraints on a compact surface of negative curvature.
We show how to use Dolgopyat's recent results to obtain a full asymptotic expansion, in
addition to the leading term given by Lalley.
We first state the properties of the stable and unstable leaves used by Chernov and
Dolgopyat; then we introduce the usual transfer operators and we prove the result with
the help of a dynamical #­function.
RESUME : Nous ’etudions un probl‘eme de d’enombrement de g’eod’esiques ferm’ees,
class’ees selon leur longueur et leur classe d'homologie, sur une surface compacte de cour­
bure n’egative. Nous expliquons comment les travaux r’ecents de Dolgopyat permettent de
donner un d’eveloppement asymptotique complet, en plus du terme principal d’ej‘a obtenu
par Lalley.
Nous commen›cons par ’enoncer les propri’et’es des feuilletages stable et instable utilis’ees

  

Source: Anantharaman, Nalini - Centre de Mathématiques Laurent Schwartz, École Polytechnique

 

Collections: Mathematics