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. 
Charles F. F. Karney (1), Alexander B. Rechester (2), Roscoe B. White   (1) ((1) Princeton University, (2) Massachusetts Ins...