Monotonous period function for equivariant differential equations with homogeneous nonlinearities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929597790027776 |
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| author | Gasull, Armengol Rojas, David |
| author_facet | Gasull, Armengol Rojas, David |
| contents | We prove that the period function of the center at the origin of the $\mathbb{Z}_k$-equivariant differential equation $\dot{z}=iz+a(z\overline{z})^nz^{k+1}, a\ne0,$ is monotonous decreasing for all $n$ and $k$ positive integers, solving a conjecture about them. We show this result as corollary of proving that the period function of the center at the origin of a sub-family of the reversible quadratic centers is monotonous decreasing as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotonous period function for equivariant differential equations with homogeneous nonlinearities Gasull, Armengol Rojas, David Dynamical Systems We prove that the period function of the center at the origin of the $\mathbb{Z}_k$-equivariant differential equation $\dot{z}=iz+a(z\overline{z})^nz^{k+1}, a\ne0,$ is monotonous decreasing for all $n$ and $k$ positive integers, solving a conjecture about them. We show this result as corollary of proving that the period function of the center at the origin of a sub-family of the reversible quadratic centers is monotonous decreasing as well. |
| title | Monotonous period function for equivariant differential equations with homogeneous nonlinearities |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.12408 |