Caputo Fractional Standard Map: Scaling Invariance Analyses

Abstract

In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<\alpha<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for which the map is chaotic. The survival probability has a short plateau followed by an exponential decay and is scaling invariant for all considered values of $\alpha$ and $K$.