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Lalley's theorem on periodic orbits of hyperbolic flows

Published online by Cambridge University Press:  01 February 1998

MARTINE BABILLOT and
FRANÇOIS LEDRAPPIER
MARTINE BABILLOT
Affiliation:
URA224, Laboratoire de Probabilités, Université Pierre & Marie Curie, 4 Place Jussieu, 75252 Paris cedex 05, France
FRANÇOIS LEDRAPPIER
Affiliation:
URA169, Centre de Mathématiques, Ecole Polytechnique, 91128 Palaiseau cedex, France
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Abstract

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We give an asymptotic estimate for the number of periodicorbits of an Anosov flow which are subject to multi-dimensional constraints.We also study their spatial distribution. For instance, we describe thedistribution of periodic orbits with respect to homology classes, for bothhomologically full Anosov flows and suspensions of Anosov transformations.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 1 , February 1998, pp. 17 - 39
Copyright
1998 Cambridge University Press