Scaling on a Dissipative Standard Mapping

Abstract

We discuss in this chapter the scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping, which is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and large time recover the results known in the literature from the phenomenological approach while a scaling for intermediate time is obtained as dependent on the initial action.