Meromorphic extensions of generalised zeta functions View Full Text


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Article Info

DATE

1986-02

AUTHORS

Mark Pollicott

ABSTRACT

In this paper we give a full description of the spectrum of the Ruelle-Perron-Frobenius operator acting on the Banach space of Holder continuous functions on a subshift of finite type (Theorem 1). These results are then used to extend the meromorphic domain of generalised zeta functions (Theorem 2). The most important application of these results is to the domain of the Smale zeta function for Axiom A flows (Theorem 3). In the course of this paper we settle questions raised by Ruelle and Sunada. More... »

PAGES

147-164

References to SciGraph publications

  • 1983-03. An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions in ISRAEL JOURNAL OF MATHEMATICS
  • 1976-10. Zeta-functions for expanding maps and Anosov flows in INVENTIONES MATHEMATICAE
  • 1976-06. Statistical mechanics of a one-dimensional lattice gas with exponential-polynomial interactions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1981-03. Conditional pressure and coding in ISRAEL JOURNAL OF MATHEMATICS
  • 1975. Equilibrium statistical mechanics of one-dimensional classical lattice systems in INTERNATIONAL SYMPOSIUM ON MATHEMATICAL PROBLEMS IN THEORETICAL PHYSICS
  • 1969-10. Applications of ergodic theory to the investigation of manifolds of negative curvature in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 1961-01. On the spectral theory of elliptic differential operators. I in MATHEMATISCHE ANNALEN
  • 1937-12. Analyse de la loi asymptotique de la distribution des nombres premiers généralisés. I in ACTA MATHEMATICA
  • 1983-12. The arithmetic and geometry of some hyperbolic three manifolds in ACTA MATHEMATICA
  • 1975-10. The ergodic theory of AxiomA flows in INVENTIONES MATHEMATICAE
  • 1985-12. Asymptotic distribution of closed geodesics in ISRAEL JOURNAL OF MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1007/bf01388795

    DOI

    http://dx.doi.org/10.1007/bf01388795

    DIMENSIONS

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