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Effect of Noise on the Standard Mapping

Charles F. F. Karney·Alexander B. Rechester·Roscoe B. White
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Abstract

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term proportional to the reciprocal of the variance of the noise term. At large values of the stochasticity parameter, the accelerator modes exhibit a universal behavior. As a result the dependence of the diffusion coefficient on the stochasticity parameter also shows some universal behavior.

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Charles F. F. Karney, Alexander B. Rechester, Roscoe B. White. 2005-01-10. Effect of Noise on the Standard Mapping. https://doi.org/10.1016/0167-2789(82)90045-8

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