A note on Hilbert 16th Problem
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916534628122624 |
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| author | Gasull, Armengol Santana, Paulo |
| author_facet | Gasull, Armengol Santana, Paulo |
| contents | Let $\mathcal{H}(n)$ be the maximum number of limit cycles that a planar polynomial vector field of degree $n$ can have. In this paper we prove that $\mathcal{H}(n)$ is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Hilbert 16th Problem Gasull, Armengol Santana, Paulo Dynamical Systems Let $\mathcal{H}(n)$ be the maximum number of limit cycles that a planar polynomial vector field of degree $n$ can have. In this paper we prove that $\mathcal{H}(n)$ is realizable by structurally stable vector fields with only hyperbolic limit cycles and that it is a strictly increasing function whenever it is finite. |
| title | A note on Hilbert 16th Problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2407.13465 |