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

  • WILLIAM PARRY (a1) and MARK POLLICOTT (a1)
Abstract

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

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[1]Artin, M. and Mazur, B.. On periodic points. Ann. of Math. 81 (1965), 8299.
[2]Bowen, R.. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math. 92 (1970), 725747.
[3]Bowen, R.. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429460.
[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), 137151.
[8]Parry, W.. Skew products of shift with a compact Lie groups. J. London Math. Soc. 56 (1997), 395404.
[9]Parry, W. and Pollicott, M.. The Chebotarov theorem for Galois coverings of Axiom A flows. Ergod. Th. & Dynam. Sys. 6 (1986), 133148.
[10]Parry, W. and Schmidt, K.. Natural coefficients and invariants for Markov-shifts. Invent. Math. 76 (1984), 1532.
[11]Sarnak, P.. Class numbers of indefinite binary quadratic forms. J. Number Theory 15 (1982), 229247.
[12]Stopple, J.. A reciprocity law for prime geodesics. J. Number Theory 29 (1988), 224230.
[13]Sunada, T.. Riemannian coverings and isospectral manifolds. Ann. of Math. 121 (1985), 169186.
[14]Sunada, T.. Tchbotarev’s density theorem for closed geodesics in a compact locally symmetric space of negative curvature. Preprint.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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