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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Leaking of orbits from the phase space of the dissipative discontinuous standard mapping

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Author(s):
de Oliveira, Juliano A. [1, 2] ; Perre, Rodrigo M. [2] ; Mendez-Bermudez, J. A. [3, 4] ; Leonel, Edson D. [1]
Total Authors: 4
Affiliation:
[1] Univ Estadual Paulista UNESP, Dept Fis, Ave 24A, 1515 Bela Vista, BR-13506900 Rio Claro, SP - Brazil
[2] Univ Estadual Paulista UNESP, Campus Sao Joao da Boa Vista, BR-13876750 Sao Joao Da Boa Vista, SP - Brazil
[3] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico
[4] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Campus Sao Carlos Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 4
Document type: Journal article
Source: Physical Review E; v. 103, n. 1 JAN 13 2021.
Web of Science Citations: 0
Abstract

We investigate the escape of particles from the phase space produced by a two-dimensional, nonlinear and discontinuous, area-contracting map. The mapping, given in action-angle variables, is parametrized by K and gamma which control the strength of nonlinearity and dissipation, respectively. We focus on two dynamical regimes, K < 1 and K >= 1, known as slow and quasilinear diffusion regimes, respectively, for the area-preserving version of the map (i.e., when gamma = 0). When a hole of hight h is introduced in the action axis we find both the histogram of escape times P-E( n) and the survival probability P-S( n) of particles to be scale invariant, with the typical escape time n(typ) = exp < ln n >; that is, both P-E(n/n(typ)) and P-S(n/n(typ)) define universal functions. Moreover, for gamma << 1, we show that n(typ) is proportional to h(2)/D, where D is the diffusion coefficient of the corresponding area-preserving map that in turn is proportional to K-5/2 and K-2 in the slow and the quasilinear diffusion regimes, respectively. (AU)

FAPESP's process: 18/14685-9 - Transport properties and bifurcation analysis in nonlinear dynamical systems
Grantee:Juliano Antonio de Oliveira
Support Opportunities: Regular Research Grants
FAPESP's process: 19/06931-2 - Random matrix theory approach to complex networks
Grantee:Francisco Aparecido Rodrigues
Support Opportunities: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
Grantee:Edson Denis Leonel
Support Opportunities: Regular Research Grants