Boundary crises and supertrack orbits in the Gauss map

• Published in: The European physical journal. ST, Special topics Special topics, 2022-04, Vol.231 (3), p.381-384
• Main Authors: Oliveira, Juliano A. de, Mendonça, Hans M. J. de, Favarim, Vitor A., Carvalho, R. Egydio de, Leonel, Edson D.
• Format: Article
• Language: English
• Subjects: Atomic; Classical and Continuum Physics; Condensed Matter Physics; Current Trends in Computational and Experimental Techniques in Nonlinear Dynamics; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Orbits; Parameters; Physics; Physics and Astronomy; Relaxation time; Review
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjs/s11734-021-00402-8

Supertrack orbits are used to investigate boundary crises in an one-dimensional, two-parameter ( ν , β ), nonlinear Gauss map. After the crises, the time evolution of the orbit is shown to be pseudo-chaotic. We investigate the chaotic transient, that is, the time an orbit spends in a region where the chaotic attractor existed prior to the crisis, and confirm it decays exponentially with time. The relaxation time is given by a power-law τ ∝ μ γ with μ = | β - β c | corresponding to the distance measured in the parameter where the crises are observed. β c is the parameter that characterizes the occurrence of a boundary crisis and the numerical value of the power measured was γ = 1 / 2 .