Summary
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.
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Pollicott, M. Meromorphic extensions of generalised zeta functions. Invent Math 85, 147–164 (1986). https://doi.org/10.1007/BF01388795
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DOI: https://doi.org/10.1007/BF01388795