Global centers of a class of cubic polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rondon Vielma, Gabriel Alexis (São Paulo State University . Institute of Biosciences, Humanities and Exact Sciences)

Date:	2024
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Global centers ; Vertical blow-up ; Polynomial differential equations
Published in:	Rendiconti del Circolo Matematico di Palermo, Vol. 73, Issue 5 (August 2024) , p. 2141-2160, ISSN 1973-4409

DOI: 10.1007/s12215-024-01034-2

Postprint 19 p, 352.3 KB

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