Attractor-repeller collision and the heterodimensional dynamics

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 Möbius 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.

References in corpus (5)

• On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators
• Homoclinic Bifurcations that Give Rise to Heterodimensional Cycles near A Saddle-Focus Equilibrium
• Conservative, Dissipative and Super-diffusive Behavior of a Particle Propelled in a Regular Flow
• Existence of Heterodimensional Cycles near Shilnikov Loops in Systems with a ${\mathbb{Z}}_2$ Symmetry
• Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization

Cited by in corpus (1)

• Depinning transition of self-propelled particles