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

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Parry, William and Pollicott, Mark. (2008) An analogue of Bauer’s theorem for closed orbits of skew products. Ergodic Theory and Dynamical Systems, Vol.28 (No.2). pp. 535-546. ISSN 0143-3857

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Official URL: http://dx.doi.org/10.1017/S0143385707000557

Abstract

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

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Algebraic number theory -- Problems, exercises, etc., Galois theory, Finite fields (Algebra), Differential equations, Hyperbolic, Differentiable dynamical systems
Journal or Publication Title:	Ergodic Theory and Dynamical Systems
Publisher:	Cambridge University Press
ISSN:	0143-3857
Date:	7 April 2008
Volume:	Vol.28
Number:	No.2
Page Range:	pp. 535-546
Identification Number:	10.1017/S0143385707000557
Status:	Peer Reviewed
Access rights to Published version:	Open Access
References:	[1] Artin, M. and Mazur, B.. On periodic points. Ann. of Math. 81 (1965), 82–99. [2] Bowen, R.. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math. 92 (1970), 725–747. [3] Bowen, R.. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429–460. [4] Buser, P.. Geometry and Spectra of Compact Riemann Surfaces (Progress in Mathematics, 106). Birkhäuser, Boston, 1992. [5] Cassels, J. and Frolich, A.. Algebraic Number Theory. Academic Press, London, 1967. [6] Narkiewicz, W.. Elementary and Analytic Theory of Algebraic Numbers. PWN, Warsaw, 1974. [7] Noorani, M. and Parry, W.. A Chebotarev theorem for finite homogeneous extensions of shifts. Bol. Soc. Brasil. Mat. 23 (1992), 137–151. [8] Parry, W.. Skew products of shift with a compact Lie groups. J. London Math. Soc. 56 (1997), 395–404. [9] Parry, W. and Pollicott, M.. The Chebotarov theorem for Galois coverings of Axiom A flows. Ergod. Th. & Dynam. Sys. 6 (1986), 133–148. [10] Parry, W. and Schmidt, K.. Natural coefficients and invariants for Markov-shifts. Invent. Math. 76 (1984), 15–32. [11] Sarnak, P.. Class numbers of indefinite binary quadratic forms. J. Number Theory 15 (1982), 229–247. [12] Stopple, J.. A reciprocity law for prime geodesics. J. Number Theory 29 (1988), 224–230. [13] Sunada, T.. Riemannian coverings and isospectral manifolds. Ann. of Math. 121 (1985), 169–186. [14] Sunada, T.. Tchbotarev’s density theorem for closed geodesics in a compact locally symmetric space of negative curvature. Preprint.
URI:	http://wrap.warwick.ac.uk/id/eprint/660