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Counting geodesics which are optimal in homology

Published online by Cambridge University Press:  22 September 2003

NALINI ANANTHARAMAN
NALINI ANANTHARAMAN
Affiliation:
Ecole Normale Supérieure, Département de Mathématiques et Applications, 45 rue d'Ulm, 75005 Paris, France (e-mail: nanantha@umpa.ens-lyon.fr)
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Abstract

On a surface of negative curvature, we study the distribution of closed geodesics which are not far from minimizing length in their homology classes. These geodesics do not have the statistical behaviour obtained by Margulis for ‘generic’ geodesics and later extended by Lalley to geodesics satisfying certain homological constraints. We cannot use the usual techniques of ‘thermodynamic formalism for Anosov flows’, but we study the problem using ideas from Aubry–Mather theory, as well as some facts of low-dimensional topology.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003 , pp. 353 - 388
Copyright
2003 Cambridge University Press

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