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Leaking from the phase space of the Riemann-Liouville fractional standard map
- Publication Year :
- 2023
-
Abstract
- In this work we characterize the escape of orbits from the phase space of the Riemann-Liouville (RL) fractional standard map (fSM). The RL-fSM, given in action-angle variables, is derived from the equation of motion of the kicked rotor when the second order derivative is substituted by a RL derivative of fractional order $\alpha$. Thus, the RL-fSM is parameterized by $K$ and $\alpha\in(1,2]$ which control the strength of nonlinearity and the fractional order of the RL derivative, respectively. Indeed, for $\alpha=2$ and given initial conditions, the RL-fSM reproduces Chirikov's standard map. By computing the survival probability $P_{\text{S}}(n)$ and the frequency of escape $P_{\text{E}}(n)$, for a hole of hight $h$ placed in the action axis, we observe two scenarios: When the phase space is ergodic, both scattering functions are scale invariant with the typical escape time $n_{\text{typ}}=\exp\langle \ln n \rangle \propto (h/K)^2$. In contrast, when the phase space is not ergodic, the scattering functions show a clear non-universal and parameter-dependent behavior.
- Subjects :
- Nonlinear Sciences - Chaotic Dynamics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2302.13008
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.chaos.2023.113532