Attractor-repeller collision and the heterodimensional dynamics
Chaotic Dynamics
2024-07-19 v1
Abstract
We study the heterodimensional dynamics in a simple map on a three-dimensional torus. This map consists of a two-dimensional driving Anosov map and a one-dimensional driven M\"obius map, and demonstrates the collision of a chaotic attractor with a chaotic repeller if parameters are varied. We explore this collision by following tangent bifurcations of the periodic orbits, and establish a regime where periodic orbits with different numbers of unstable directions coexist in a chaotic set. For this situation, we construct a heterodimensional cycle connecting these periodic orbits. Furthermore, we discuss properties of the rotation number and of the nontrivial Lyapunov exponent at the collision and in the heterodimensional regime.
Cite
@article{arxiv.2305.18172,
title = {Attractor-repeller collision and the heterodimensional dynamics},
author = {V. Chigarev and A. Kazakov and A. Pikovsky},
journal= {arXiv preprint arXiv:2305.18172},
year = {2024}
}