New families of global cubic centers
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Serantola, Leonardo P. (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)

Date:	2024
Abstract:	An equilibrium point p of a differential system in the plane R2 is a center if there exists a neighbourhood U of p such that U\{p} is filled with periodic orbits. A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the problem of distinguishing between a focus and a center. A global center is a center p such that R2\{p} is filled with periodic orbits. Another difficult problem in the qualitative theory of differential systems in R2 is to distinguish inside a family of centers the ones which are global. Lloyd, Pearson and Romanovsky characterized when the origin of coordinates is a center for the family of cubic polynomial differential systems x˙=y-Cx+B+2Dxy+Cy+Px+Gxy-H+3Pxy+Ky,y˙=-x+Dx+E+2Cxy-Dy-Kx-H+3Pxy-Gxy+Py. Here we characterize when the origin of this family of differential system is a global center.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Center ; Global center ; Cubic polynomial differential systems
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 18 (December 2024) , p. 1454-1469, ISSN 2316-9028

DOI: 10.1007/s40863-024-00411-0

Postprint 14 p, 300.3 KB

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