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...

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Bibliographic Details
Authors: Gasull, Armengol|||0000-0002-1719-8231, Rojas, David|||0000-0001-7247-4705
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
Description
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.