Year: 2025
Type: article
Abstract: In this article, we study a two-parameter family of rotating rank-one maps defined on $ {\mathbb{S}}^1\times [1, 1+b]\times {\mathbb{S}}^1 $, $ b\gtrsim 0 $, whose dynamics is characterised by a skew-product of a family of planar maps exhibiting rank-one strange attractors coupled with an Arnold family of circle maps. The main result is about the dynamics on the skew-product, which is governed by the existence and prevalence of strange attractors in the corresponding resonance tongues of the Arnold family. The strange attractors carry the unique physical measure of the system, which determines the behaviour of Lebesgue-almost all initial conditions.This phenomenon can be considered as the transition dynamics from a strange attractor with one positive Lyapunov exponent to hyperchaos. Besides an analytical rigorous proof, we illustrate the main results with numerical simulations. We also conjecture how persistent hyperchaos can be obtained.
DOI: 10.3934/dcds.2025037
Institutions: Universidade do Porto, Centro de Matemática
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408801353