Unbounded dynamics for vector fields
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929711908651008 |
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| author | Igra, Eran |
| author_facet | Igra, Eran |
| contents | Consider a three-dimensional vector field $F$ which generates a finite number of fixed points - what can we say on its unbounded dynamics? In this paper we tackle this question, and prove sufficient conditions for $F$ to have fixed points with unbounded invariant manifolds. Following that, we use these results to study the dynamics of the Genesio-Tesi system, the Belousov-Zhabotinsky reaction, and the Michelson system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unbounded dynamics for vector fields Igra, Eran Dynamical Systems Classical Analysis and ODEs 34A26, 34A34, 34C05, 34C11, 34C45 Consider a three-dimensional vector field $F$ which generates a finite number of fixed points - what can we say on its unbounded dynamics? In this paper we tackle this question, and prove sufficient conditions for $F$ to have fixed points with unbounded invariant manifolds. Following that, we use these results to study the dynamics of the Genesio-Tesi system, the Belousov-Zhabotinsky reaction, and the Michelson system. |
| title | Unbounded dynamics for vector fields |
| topic | Dynamical Systems Classical Analysis and ODEs 34A26, 34A34, 34C05, 34C11, 34C45 |
| url | https://arxiv.org/abs/2502.08300 |