The leading Ruelle resonances of chaotic maps

Details The leading Ruelle resonances of chaotic maps The leading Ruelle resonances of chaotic maps

2000-05-16

arxiv.org/abs/nlin/0005030v1

Phys. Rev. E 62, 1977 (2000)

Nonlinear Sciences

Chaotic Dynamics

5 pages, 4 figures included. To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.62.1977

The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, the roots of the equation $z^4=\gamma$, where $\gamma$ is a positive number which characterizes the amount of stochasticity of the map. The results are verified by numerical computations, and the implications to the form factor of the corresponding quantum maps are discussed.

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