Charles Karney: Publication 28/85, Karney(1982)

C. F. F. Karney, A. B. Rechester, and R. B. White.
Effect of noise on the standard mapping.
Physica, 4D(3):425–438, March 1982.
E-print: arXiv:nlin.CD/0501021 (Mirror).
Princeton Univ. Rept. PPPL-1752 (Mar. 1981) 25 pp.
Reprint: physd82
DOI: 10.1016/0167-2789(82)90045-8
BibTeX Entry

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.