The Uniform Isochronous Centers with Homogeneous Nonlinearities of Degree 5

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...

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Detalles Bibliográficos
Autores: Dong, Guangfeng, Llibre, Jaume|||0000-0002-9511-5999
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:318292
Acceso en línea:https://ddd.uab.cat/record/318292
https://dx.doi.org/urn:doi:10.1007/s10883-025-09734-3
Access Level:acceso embargado
Palabra clave:Uniform isochronous center
Polynomial vector field
Phase portrait
Separatrix configuration
Periodic orbit
Descripción
Sumario: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.