Reversible nilpotent centers with cubic nonlinearities
Bacelar, Leandro (Universidade de São Paulo)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	A real analytic differential system having a center at the origin of coordinates after a linear change of variables and a rescaling of the time can be written in one of the following three forms: (Formula presented. ) called a linear type center, (Formula presented. ) called a nilpotent center, and (Formula presented. ) called a degenerate center, where X2(x,y) and Y2(x,y) are real analytic functions without constant and linear terms, defined in a neighborhood of the origin. While there are many papers dedicated to study phase portraits of different classes of linear type centers, few papers studied the phase portraits of the nilpotent and degenerate centers. Here we classify the global phase portraits in the Poincaré disc of reversible nilpotent centers with cubic nonlinearities.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Cubic polynomials differential systems ; Reversible centers ; Nilpotent centers
Published in:	Rendiconti del Circolo Matematico di Palermo, Vol. 74 (June 2025) , art. 138, ISSN 1973-4409

DOI: 10.1007/s12215-025-01256-y

25 p, 629.9 KB

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