Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-28T16:08:41.326Z Has data issue: false hasContentIssue false

An analogue of Bauer’s theorem for closed orbits of skew products

Published online by Cambridge University Press:  01 April 2008

WILLIAM PARRY
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK (email: m.pollicott@warwick.ac.uk)
MARK POLLICOTT
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK (email: m.pollicott@warwick.ac.uk)

Abstract

In this article we prove an analogue of Bauer’s theorem from algebraic number theory in the context of hyperbolic systems.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Artin, M. and Mazur, B.. On periodic points. Ann. of Math. 81 (1965), 8299.CrossRefGoogle Scholar
[2]Bowen, R.. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math. 92 (1970), 725747.CrossRefGoogle Scholar
[3]Bowen, R.. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429460.CrossRefGoogle Scholar
[4]Buser, P.. Geometry and Spectra of Compact Riemann Surfaces (Progress in Mathematics, 106). Birkhäuser, Boston, 1992.Google Scholar
[5]Cassels, J. and Frolich, A.. Algebraic Number Theory. Academic Press, London, 1967.Google Scholar
[6]Narkiewicz, W.. Elementary and Analytic Theory of Algebraic Numbers. PWN, Warsaw, 1974.Google Scholar
[7]Noorani, M. and Parry, W.. A Chebotarev theorem for finite homogeneous extensions of shifts. Bol. Soc. Brasil. Mat. 23 (1992), 137151.CrossRefGoogle Scholar
[8]Parry, W.. Skew products of shift with a compact Lie groups. J. London Math. Soc. 56 (1997), 395404.CrossRefGoogle Scholar
[9]Parry, W. and Pollicott, M.. The Chebotarov theorem for Galois coverings of Axiom A flows. Ergod. Th. & Dynam. Sys. 6 (1986), 133148.CrossRefGoogle Scholar
[10]Parry, W. and Schmidt, K.. Natural coefficients and invariants for Markov-shifts. Invent. Math. 76 (1984), 1532.CrossRefGoogle Scholar
[11]Sarnak, P.. Class numbers of indefinite binary quadratic forms. J. Number Theory 15 (1982), 229247.CrossRefGoogle Scholar
[12]Stopple, J.. A reciprocity law for prime geodesics. J. Number Theory 29 (1988), 224230.CrossRefGoogle Scholar
[13]Sunada, T.. Riemannian coverings and isospectral manifolds. Ann. of Math. 121 (1985), 169186.CrossRefGoogle Scholar
[14]Sunada, T.. Tchbotarev’s density theorem for closed geodesics in a compact locally symmetric space of negative curvature. Preprint.Google Scholar