Effect of noise on the standard mapping
Charles F. F. Karney, Alexander B. Rechester, Roscoe B. White · 1981
The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator models (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 stochasticity parameter also shows some universal behavior.