Monotonous Period Function for Equivariant Differential Equations with Homogeneous Nonlinearities
We prove that the period function of the center at the origin of the Zk-equivariant differential equation z˙= iz + a(zz¯)nzk + 1, a ≠ 0, 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 o...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:318558 |
| Acceso en línea: | https://ddd.uab.cat/record/318558 https://dx.doi.org/urn:doi:10.1007/s00009-025-02879-2 |
| Access Level: | acceso abierto |
| Palabra clave: | Period function Reversible quadratic centers Zk-equivariant differential equations |
| Sumario: | We prove that the period function of the center at the origin of the Zk-equivariant differential equation z˙= iz + a(zz¯)nzk + 1, a ≠ 0, 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. |
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