Leading pollicott-ruelle resonances and transport in area-preserving maps |
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Authors: | Venegeroles Roberto |
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Institution: | Instituto de Física, Universidade de S?o Paulo, S?o Paulo, Brazil. rveneger@fma.if.usp.br |
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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 a nonlinear rotation number. Numerical simulations support this formula. |
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