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Error terms for closed orbits of hyperbolic flows

Published online by Cambridge University Press:  30 March 2001

MARK POLLICOTT  and
RICHARD SHARP
MARK POLLICOTT
Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, UK
RICHARD SHARP
Affiliation:
Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, UK
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Abstract

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In this paper we obtain a polynomial error term for the closed orbit counting function associated to certain hyperbolic flows. In the case of weak-mixing transitive Anosov flows no further conditions are required; for general weak-mixing hyperbolic flows a diophantine condition on the periods of the closed orbits is required.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 545 - 562
Copyright
2001 Cambridge University Press