Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps

Abstract

The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula for the diffusion coefficient D is derived without any high stochasticity approximation and a new effect emerges: The angular evolution can induce fast or slow modes of diffusion even in the high stochasticity regime. The behavior of D is examined for three particular cases: (i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example of a map with nonlinear rotation number. Numerical simulations support this formula.

arXiv comment5 pages, 1 figure

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Cited by in corpus (7)

• Survey on the role of accelerator modes for anomalous diffusion: The case of the standard map
• Calculation of Superdiffusion for the Chirikov-Taylor Model
• Stochastic stability of Pollicott-Ruelle resonances
• Leading Pollicott-Ruelle Resonances for Chaotic Area-Preserving Maps
• Capturing correlations in chaotic diffusion by approximation methods
• Non-Gaussian features of chaotic Hamiltonian transport
• A hybrid method for calculation of Ruelle-Pollicott resonances