Essential dynamics in chaotic attractors
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916589936312320 |
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| author | Igra, Eran |
| author_facet | Igra, Eran |
| contents | We prove that if a smooth vector field $F$ of $S^3$ generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic knot. Consequentially, we then associate a Template with the flow dynamics - regardless of whether $F$ satisfies any hyperbolicity condition or not. In addition, inspired by the Thurston-Nielsen Classification Theorem, we also conclude topological criteria for the existence of chaotic dynamics for three-dimensional flows - which we apply to study both the Rössler and Lorenz attractors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Essential dynamics in chaotic attractors Igra, Eran Dynamical Systems Classical Analysis and ODEs 37C10, 37C27, 37C29, 37C70, 37B99, 37G35 We prove that if a smooth vector field $F$ of $S^3$ generates a sufficiently complicated heteroclinic knot, the flow also generates infinitely many periodic orbits, which persist under smooth perturbations which preserve the heteroclinic knot. Consequentially, we then associate a Template with the flow dynamics - regardless of whether $F$ satisfies any hyperbolicity condition or not. In addition, inspired by the Thurston-Nielsen Classification Theorem, we also conclude topological criteria for the existence of chaotic dynamics for three-dimensional flows - which we apply to study both the Rössler and Lorenz attractors. |
| title | Essential dynamics in chaotic attractors |
| topic | Dynamical Systems Classical Analysis and ODEs 37C10, 37C27, 37C29, 37C70, 37B99, 37G35 |
| url | https://arxiv.org/abs/2411.08571 |