  We study the scaling properties of discontinuous maps by analyzing the
average value of the squared action variable $I^2$. We focus our study on two
dynamical regimes separated by the critical value $K_c$ of the control
parameter $K$: the slow diffusion ($K<K_c$) and the quasilinear diffusion
($K>K_c$) regimes. We found that the scaling of $I^2$ for discontinuous maps
when $K\ll K_c$ and $K\gg K_c$ obeys the same scaling laws, in the appropriate
limits, than Chirikov's standard map in the regimes of weak and strong
nonlinearity, respectively. However, due to absence of KAM tori, we observed in
both regimes that $I^2\propto nK^\beta$ for $n\gg 1$ (being $n$ the $n$-th
iteration of the map) with $\beta\approx 5/2$ when $K\ll K_c$ and $\beta\approx
2$ for $K\gg K_c$.
