Attractor-repeller collision and the heterodimensional dynamics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916328925822976 |
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| author | Chigarev, V. Kazakov, A. Pikovsky, A. |
| author_facet | Chigarev, V. Kazakov, A. Pikovsky, A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18172 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Attractor-repeller collision and the heterodimensional dynamics Chigarev, V. Kazakov, A. Pikovsky, A. Chaotic Dynamics 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. |
| title | Attractor-repeller collision and the heterodimensional dynamics |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2305.18172 |