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Zeta-functions for expanding maps and Anosov flows

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Abstract

Given a real-analytic expanding endomorphism of a compact manifoldM, a meromorphic zeta function is defined on the complex-valued real-analytic functions onM. A zeta function for Anosov flows is shown to be meromorphic if the flow and its stable-unstable foliations are real-analytic.

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  1. I.H.E.S., 35, Route de Chartres, F-91440, Bures-sur-Yvette, France

    David Ruelle

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  1. David Ruelle
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Ruelle, D. Zeta-functions for expanding maps and Anosov flows. Invent Math 34, 231–242 (1976). https://doi.org/10.1007/BF01403069

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  • DOI: https://doi.org/10.1007/BF01403069

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