Leading Pollicott-Ruelle Resonances for Chaotic Area-Preserving Maps
arXiv:0710.4779 · doi:10.1103/PhysRevE.77.027201
Abstract
Recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime. The relaxation rates, which lead the decay of probability distributions and correlation functions, are related to the classical evolution resolvent (Perron-Frobenius operator) pole logarithm, the so called Pollicott-Ruelle resonances. In this Brief Report, the leading Pollicott-Ruelle resonances are calculated analytically for a general class of area-preserving maps. Besides the leading resonances related to the diffusive modes of momentum dynamics (slow rate), we also calculate the leading faster rate, related to the angular correlations. The analytical results are compared to the existing results in the literature.
arXiv comment6 pages, 1 figure. See also: R. Venegeroles, Phys. Rev. Lett. 99, 014101 (2007) or arXiv:nlin/0608067v2
References in corpus (13)
- Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory
- Quantum fingerprints of classical Ruelle-Pollicot resonances
- Frobenius-Perron Resonances for Maps with a Mixed Phase Space
- Relaxation and Diffusion for the Kicked Rotor
- Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
- Classical decays in decoherent quantum maps
- Relaxation to the Invariant Density for Kicked Rotor
- On the long-time behavior of spin echo and its relation to free induction decay
- The leading Ruelle resonances of chaotic maps
- Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
- Periodic orbit spectrum in terms of Ruelle--Pollicott resonances
- Locating Pollicott-Ruelle resonances in chaotic dynamical systems: A class of numerical schemes
- Non-Gaussian features of chaotic Hamiltonian transport
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- Response Dynamics of Alkali Metal-Noble Gas Hybrid Trispin System
- Non-Gaussian features of chaotic Hamiltonian transport
- A hybrid method for calculation of Ruelle-Pollicott resonances