Onset of Diffusion and Universal Scaling in Chaotic Systems

A new type of universality associated with the onset of a deterministic diffusion for systems described by iterative one-dimensional maps is reported. The diffusion coefficient $D$ plays the role of an order parameter with a universal critical exponent. For the presence of external noise, the existence of a universal scaling function $d$ is shown. An analytic expression is derived for $d$ which is in good agreement with results of a numerical experiment.