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

Author(s)

Mendez-Bermudez, J. A. ; Peralta-Martinez, Kevin ; Sigarreta, Jose M. ; Leonel, Edson D.

• Document type: Journal article
• Source: CHAOS SOLITONS & FRACTALS; v. 172, p. 7-pg., 2023-05-22.

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... Thus, the RL-fSM is parameterized by Kappa and alpha is an element of (1, 2] which control the strength of nonlinearity and the fractional order of the RL derivative, respectively. Indeed, for = 2 and given initial conditions, the RL-fSM reproduces Chirikov's standard map. By computing the survival probability P-S(n) and the frequency of escape P-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(typ) = exp < ln n > alpha ( h/Kappa)(2). In contrast, when the phase space is not ergodic, the scattering functions show a clear non-universal and parameter-dependent behavior. (AU)

• FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
• Grantee: Edson Denis Leonel
• Support Opportunities: Regular Research Grants