Ruelle-Pollicott resonances for real analytic hyperbolic map

Details Ruelle-Pollicott resonances for real analytic hyperbolic map Ruelle-Pollicott resonances for real analytic hyperbolic map

2006-01-04

arxiv.org/abs/nlin/0601010v2

Nonlinearity Vol. 19, p. 1233-1252, 2006

Nonlinear Sciences

Chaotic Dynamics

26 pages, 7 figures

Scientific paper

10.1088/0951-7715/19/6/002

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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