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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:318558 |
| Online Access: | https://ddd.uab.cat/record/318558 https://dx.doi.org/urn:doi:10.1007/s00009-025-02879-2 |
| Access Level: | Open access |
| Keyword: | Period function Reversible quadratic centers Zk-equivariant differential equations |
| Summary: | 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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