https://doi.org/10.1140/epjs/s11734-021-00402-8
Review
Boundary crises and supertrack orbits in the Gauss map
1
Universidade Estadual Paulista (UNESP), Câmpus de São João da Boa Vista, Av. Profa. Isette Corrêa Fontão, 505, 13876-750, SP, Brazil
2
The Abdus Salam - ICTP, Strada Costiera, 11-34151, Trieste, Italy
3
Departamento de Estatística, Matemática Aplicada e Computação, Universidade Estadual Paulista (UNESP), Av. 24A, 1515, 13506-900, Rio Claro-SP, Brazil
4
Departamento de Física, Universidade Estadual Paulista (UNESP), Av. 24A, 1515, 13506-900, Rio Claro-SP, Brazil
Received:
30
June
2021
Accepted:
16
December
2021
Published online:
25
January
2022
Supertrack orbits are used to investigate boundary crises in an one-dimensional, two-parameter (
), 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 
with 
corresponding to the distance measured in the parameter where the crises are observed. 
is the parameter that characterizes the occurrence of a boundary crisis and the numerical value of the power measured was 
.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
