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Ruelle-Pollicott resonances for real analytic hyperbolic map

Frederic Faure·Nicolas Roy
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Abstract

We study two simple real analytic uniformly hyperbolic dynamical systems: expanding maps on the circle S1 and hyperbolic maps on the torus T2. We show that the Ruelle-Pollicott resonances which describe time correlation functions of the chaotic dynamics can be obtained as the eigenvalues of a trace class operator in Hilbert space L2(S1) or L2(T2) respectively. The trace class operator is obtained by conjugation of the Ruelle transfer operator in a similar way quantum resonances are obtained in open quantum systems. We comment this analogy.

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Frederic Faure, Nicolas Roy. 2006-04-21. Ruelle-Pollicott resonances for real analytic hyperbolic map. https://doi.org/10.1088/0951-7715%2F19%2F6%2F002

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