Global centers of a class of cubic polynomial differential systems

A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Rondon Vielma, Gabriel Alexis|||0000-0001-8594-9327
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:303176
Acceso en línea:https://ddd.uab.cat/record/303176
https://dx.doi.org/urn:doi:10.1007/s12215-024-01034-2
Access Level:acceso abierto
Palabra clave:Global centers
Vertical blow-up
Polynomial differential equations
Descripción
Sumario:A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w = x + iy and A ∈ C for k = 3, 4, 5, 6.