Nonsingular structural stable chaotic 3-flows of attractor-repeller type
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909823006670848 |
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| author | Lai, Zhentao Medvedev, V. Yu, Bin Zhuzhoma, E. |
| author_facet | Lai, Zhentao Medvedev, V. Yu, Bin Zhuzhoma, E. |
| contents | We show that any orientable closed 3-manifold $M$ admits structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For $M=\mathbb{S}^3$, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure eight knot. When a link consists of a unique repelling periodic trajectory (not necessarily a figure eight knot), we prove that this trajectory cannot be a torus knot. For any closed 3-manifold $M$, we show that there does not admit any structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and a repelling periodic trajectory so that the repelling periodic trajectory is a trivial knot (i.e., it bounds a disk in $M$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonsingular structural stable chaotic 3-flows of attractor-repeller type Lai, Zhentao Medvedev, V. Yu, Bin Zhuzhoma, E. Dynamical Systems 37D15, 57R50 We show that any orientable closed 3-manifold $M$ admits structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For $M=\mathbb{S}^3$, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure eight knot. When a link consists of a unique repelling periodic trajectory (not necessarily a figure eight knot), we prove that this trajectory cannot be a torus knot. For any closed 3-manifold $M$, we show that there does not admit any structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and a repelling periodic trajectory so that the repelling periodic trajectory is a trivial knot (i.e., it bounds a disk in $M$). |
| title | Nonsingular structural stable chaotic 3-flows of attractor-repeller type |
| topic | Dynamical Systems 37D15, 57R50 |
| url | https://arxiv.org/abs/2510.02704 |