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arXiv · 1410.5516

Pollicott-Ruelle resonances for open systems

Semyon Dyatlov·Colin Guillarmou
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Abstract

We define Pollicott-Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of the meromorphic continuation of the resolvent of the generator of the flow and they describe decay of classical correlations. As an application, we show that the Ruelle zeta function extends meromorphically to the entire complex plane.

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Semyon Dyatlov, Colin Guillarmou. 2016-04-03. Pollicott-Ruelle resonances for open systems. https://doi.org/10.1007/s00023-016-0491-8

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