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- Title
Sub-diffusive behavior in the Standard Map.
- Authors
Palmero, Matheus S.; Díaz, Gabriel I.; Caldas, Iberê L.; Sokolov, Igor M.
- 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.
- Subjects
SOCIAL norms; HEAT equation; DYNAMICAL systems; PROBLEM solving; RANDOM walks
- Publication
European Physical Journal: Special Topics, 2021, Vol 230, Issue 14/15, p2765
- ISSN
1951-6355
- Publication type
Article
- DOI
10.1140/epjs/s11734-021-00165-2