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Anosov flows and dynamical Zeta functions
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Giulietti, Paolo, Liverani, Carlangelo and Pollicott, Mark (2013) Anosov flows and dynamical Zeta functions. Annals of Mathematics, 178 (2). 687-773 . doi:10.4007/annals.2013.178.2.6 ISSN 0003-486X.
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Official URL: http://dx.doi.org/10.4007/annals.2013.178.2.6
Abstract
We study the Ruelle and Selberg zeta functions for Cr Anosov flows, r>2, on a compact smooth manifold. We prove several results, the most remarkable being: (a) for Cā flows the zeta function is meromorphic on the entire complex plane; (b) for contact flows satisfying a bunching condition (e.g. geodesic flows on manifolds of negative curvature better than 19-pinched) the zeta function has a pole at the topological entropy and is analytic in a strip to its left; (c) under the same hypotheses as in (b) we obtain sharp results on the number of periodic orbits. Our arguments are based on the study of the spectral properties of a transfer operator acting on suitable Banach spaces of anisotropic currents.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annals of Mathematics | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 0003-486X | ||||
Official Date: | 6 September 2013 | ||||
Dates: |
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Volume: | 178 | ||||
Number: | 2 | ||||
Page Range: | 687-773 | ||||
DOI: | 10.4007/annals.2013.178.2.6 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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