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

J.A. Méndez-Bermúdez, Kevin Peralta-Martinez, José M. Sigarreta and Edson D. Leonel

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

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 α. Thus, the RL-fSM is parameterized by K and α∈(1,2] which control the strength of nonlinearity and the fractional order of the RL derivative, respectively. Indeed, for α=2 and given initial conditions, the RL-fSM reproduces Chirikov’s standard map. By computing the survival probability PS(n) and the frequency of escape PE(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 ntyp=exp〈lnn〉∝(h/K)2. In contrast, when the phase space is not ergodic, the scattering functions show a clear non-universal and parameter-dependent behavior.

Keywords: Fractional standard map; Classical scattering; Nonlinear dynamics (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004332

DOI: 10.1016/j.chaos.2023.113532

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