Leaking from the phase space of the Riemann–Liouville fractional standard map

In this work we characterize the escape of orbits from phase space Riemann–Liouville (RL) fractional standard map (fSM). The RL-fSM, given in action–angle variables, is derived equation motion kicked rotor when second order derivative substituted by a RL α. Thus, RL-fSM parameterized K and α∈(1,2] which control strength nonlinearity derivative, respectively. Indeed, for α=2 initial conditions, reproduces Chirikov’s map. By computing survival probability PS(n) frequency PE(n), hole hight h placed action axis, observe two scenarios: When ergodic, both scattering functions are scale invariant with typical time ntyp=exp〈lnn〉∝(h/K)2. contrast, not show clear non-universal parameter-dependent behavior.