Title: Universal centres and composition conditions
Abstract: Proceedings of the London Mathematical SocietyVolume 106, Issue 3 p. 481-507 Articles Universal centres and composition conditions Jaume Giné, Jaume Giné [email protected] Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, Lleida, Catalonia, 25001 SpainSearch for more papers by this authorMaite Grau, Corresponding Author Maite Grau [email protected] Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, Lleida, Catalonia, 25001 [email protected] for more papers by this authorJaume Llibre, Jaume Llibre [email protected] Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Catalonia, 08193 SpainSearch for more papers by this author Jaume Giné, Jaume Giné [email protected] Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, Lleida, Catalonia, 25001 SpainSearch for more papers by this authorMaite Grau, Corresponding Author Maite Grau [email protected] Departament de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, Lleida, Catalonia, 25001 [email protected] for more papers by this authorJaume Llibre, Jaume Llibre [email protected] Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Catalonia, 08193 SpainSearch for more papers by this author First published: 11 September 2012 https://doi.org/10.1112/plms/pds050Citations: 22 2010 Mathematics Subject Classification 34C25, 34C07 (primary). The first and second authors are partially supported by a MICINN/FEDER grant number MTM2011-22877 and by a Generalitat de Catalunya grant number 2009SGR 381. The third author is partially supported by a MICINN/ FEDER grant number MTM2008-03437, by a Generalitat de Catalunya grant number 2009SGR 410 and by ICREA Academia. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract In this paper, we characterize the universal centres of the ordinary differential equations d ρ / d θ = ∑ i = 1 ∞ a i ( θ ) ρ i + 1 , where ai(θ) are trigonometric polynomials, in terms of the composition conditions. These centres are closely related with the classical Poincaré centre problem for planar analytic differential systems. Additionally, we show that the notion of universal centre is not invariant under changes of variables, and we also provide different families of universal centres. Finally, we characterize all the universal centres for the quadratic polynomial differential systems. Citing Literature Volume106, Issue3March 2013Pages 481-507 RelatedInformation