Effect of Noise on the Standard Mapping

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.Comment: Plain TeX, 18 pages, 4 figure

Physica, 4D(3), 425–438 (Mar. 1982) EFFECT OF NOISE ON THE STANDARD MAPPING

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. Key words: standard mapping; accelerator modes; area-preserving maps; diffusion; long-time correlations. – 1 – – 2 – 1