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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.)

Sub-diffusive behavior in the Standard Map

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Author(s):
Palmero, Matheus S. [1] ; Diaz, I, Gabriel ; Caldas, Ibere L. [2] ; Sokolov, Igor M. [3]
Total Authors: 4
Affiliation:
[1] Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil
[2] Diaz, Gabriel, I, Univ Sao Paulo, Inst Fis, Sao Paulo, SP - Brazil
[3] Humboldt Univ, Inst Phys, Berlin - Germany
Total Affiliations: 3
Document type: Journal article
Source: European Physical Journal-Special Topics; v. 230, n. 14-15, p. 2765-2773, OCT 2021.
Web of Science Citations: 1
Abstract

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that trajectories started from special initial conditions, close to unstable periodic orbits, exhibit sub-diffusion due to stickiness, and can be modeled as a continuous-time random walk. Additionally, we choose a variant of the Ulam method to numerically approximate the Perron-Frobenius operator for the map, allowing us to calculate the exponent of anomalous diffusion by solving an eigenvalue problem and comparing its time dependence to the solution of the fractional diffusion equation. The results here corroborate other findings in the literature of anomalous transport in Hamiltonian maps and can be suitable to describe transport properties of other dynamical systems. (AU)

FAPESP's process: 18/03000-5 - Chaotic transport in symplectic maps: Applications in plasma
Grantee:Matheus Palmero Silva
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 18/03211-6 - Non linear dynamics
Grantee:Iberê Luiz Caldas
Support Opportunities: Research Projects - Thematic Grants