Centers for the Kukles homogeneous systems with odd degree
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Instituto Superior Técnico (Lisboa). Departamento de Matemática)

Date:	2015
Abstract:	For the polynomial differential system x ̇ = −y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We prove both conjectures for all n odd.
Grants:	Ministerio de Economía y Competitividad MTM2011-22877 Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 European Commission 316338 European Commission 318999
Note:	Agraïments: FEDER-UNAB-10-4E-378. The third author is supported by Portuguese National Funds through FCT - Fundação para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Bautin method ; Complex center-focus problem ; Lyapunov constants
Published in:	Bulletin of the London Mathematical Society, Vol. 47 Núm. 2 (2015) , p. 315-324, ISSN 1469-2120

DOI: 10.1112/blms/bdv005

Postprint 13 p, 800.0 KB

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