Dynamics and Statistics of Weak Chaos in a 4–D Symplectic Map

Bountis, Tassos, Kaloudis, Konstantinos and Christodoulidi, Helen (2023) Dynamics and Statistics of Weak Chaos in a 4–D Symplectic Map. Working Paper. Springer.

Dynamics and Statistics of Weak Chaos in a 4–D Symplectic Map
Author's Accepted Manuscript
[img] PDF
Dynamics_and_Statistics_4D_Symplectic_Map.pdf - Whole Document
Restricted to Repository staff only

Item Type:Paper or Report (Working Paper)
Item Status:Live Archive


The important phenomenon of “stickiness” of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics, celestial mechanics and accelerator dynamics. Most of the work to date has focused on two-degree of freedom Hamiltonian models often represented by two-dimensional (2D) area preserving maps. In this paper, we extend earlier results using a 4–dimensional extension of the 2D MacMillan map, and show that a symplectic model of two coupled MacMillan maps also exhibits stickiness phenomena in limited regions of phase space. To this end, we employ probability distributions in the sense of the Central Limit Theorem to demonstrate that, as in the 2D case, sticky regions near the origin are also characterized by “weak” chaos and Tsallis entropy, in sharp contrast to the “strong” chaos that extends over much wider domains and is described by Boltzmann Gibbs statistics. Remarkably, similar stickiness phenomena have been observed in higher dimensional Hamiltonian systems around unstable simple periodic orbits at various values of the total energy of the system.

Keywords:Coupled MacMillan maps, Boltzmann Gibbs and Tsallis entropies, weak and strong chaos
Subjects:G Mathematical and Computer Sciences > G120 Applied Mathematics
Divisions:College of Science > School of Mathematics and Physics
Related URLs:
ID Code:54131
Deposited On:30 May 2023 11:03

Repository Staff Only: item control page