The center problem for the class of Λ- Ω differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Ramírez, Valentín (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2020
Abstract:	The center problem, i. e. distinguish between a focus and a center, is a classical problem in the qualitative theory of planar differential equations which go back to Darboux, Poincaré and Liapunov. Here we solve the center problem for the class of planar analytic or polynomial differential systems x˙= −y + X = −y + ∑j=2k Xj, y˙= x + Y = x + ∑j=2k Yj, k≤∞, where Xj = Xj(x,y)and Yj = Yj(x,y) are homogenous polynomials of degree j>1, under the condition (x2+y2)(∂X∂x+∂Y∂y) = μ(xX + yY) with μ∈R∖{0}. Moreover we prove that these centers are weak centers, and additionally we provide their first integrals.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Ministerio de Ciencia e Innovación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	First integral ; Poincaré-Liapunov first integral ; Analytic planar differential system ; Polynomial differential system ; Weak center
Published in:	Rendiconti del Circolo Matematico di Palermo, vol. 70 (October 2020) p. 1483-1499, ISSN 1973-4409

DOI: 10.1007/s12215-020-00568-5

Postprint 18 p, 698.2 KB

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