The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5
Dong, Guangfeng (Jinan University. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	The interest in studying the uniform isochronous centers goes back to C. Huygens in the XVII century. Since then, many papers have been published on this subject. In particular, the phase portraits of the polynomial uniform isochronous center up to degree four have been classified. In this paper, we classify the topological phase portraits of polynomial differential systems with a uniform isochronous center, whose nonlinear part is a homogeneous polynomial of degree 5. We prove that there are three distinct topological phase portraits in the Poincaré disc for such polynomial differential systems.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Uniform isochronous center ; Polynomial vector field ; Phase portrait ; Separatrix configuration ; Periodic orbit
Published in:	Journal of Dynamical and Control Systems, Vol. 31, Issue 2 (June 2025) , art. 11, ISSN 1573-8698

DOI: 10.1007/s10883-025-09734-3

Available from: 2026-06-30 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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