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The Chebotarov theorem for Galois coverings of Axiom A flows

Published online by Cambridge University Press:  19 September 2008

William Parry  and
Mark Pollicott
William Parry
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England
Mark Pollicott
Affiliation:
Department of Mathematics, University of Edinburgh, Edinburgh, EH9 3JZ, Scotland
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Abstract

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We consider G (Galois) coverings of Axiom A flows (restricted to basic sets) and prove an analogue of Chebotarev's theorem. The theorem provides an asymptotic formula for the number of closed orbits whose Frobenius class is a given conjugacy class in G. An application answers a question raised by J. Plante. The basic method is then extended to compact group extensions and applied to frame bundle flows defined on manifolds of variable negative curvature.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 133 - 148
Copyright
Copyright © Cambridge University Press 1986

References

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