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

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

2006-08-30

arxiv.org/abs/nlin/0608067v2

Phys. Rev. Lett. 99, 014101 (2007)

Nonlinear Sciences

Chaotic Dynamics

5 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.99.014101

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.

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