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arXiv · 2305.18172

Attractor-repeller collision and the heterodimensional dynamics

V. Chigarev·A. Kazakov·A. Pikovsky
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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.

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V. Chigarev, A. Kazakov, A. Pikovsky. 2023-05-29. Attractor-repeller collision and the heterodimensional dynamics. https://doi.org/10.1063/5.0144672

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