Limit cycles and invariant algebraic curves
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918265532448768 |
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| author | Gasull, Armengol Santana, Paulo |
| author_facet | Gasull, Armengol Santana, Paulo |
| contents | We give lower bounds in terms of~$n,$ for the number of limit cycles of polynomial vector fields of degree~$n,$ having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles we obtain a new recurrent property for the Hilbert numbers. Finally, we apply our results to two important families of models: Kolmogorov systems and a general family of systems appearing in Game Theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit cycles and invariant algebraic curves Gasull, Armengol Santana, Paulo Dynamical Systems We give lower bounds in terms of~$n,$ for the number of limit cycles of polynomial vector fields of degree~$n,$ having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles we obtain a new recurrent property for the Hilbert numbers. Finally, we apply our results to two important families of models: Kolmogorov systems and a general family of systems appearing in Game Theory. |
| title | Limit cycles and invariant algebraic curves |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.11705 |