Universal centers and composition conditions
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Grau, Maite (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	In this paper we characterize the universal centers of the ordinary differential equations dρ/dθ =∑∞i=1 ai(θ)ρi+1, where ai(θ) are trigonometric polynomials, in terms of the composition conditions. These centers are closely related with the classical Poincaré center problem for planar analytic differential systems. Additionally we show that the notion of universal center is not invariant under changes of variables, and we also provide different families of universal centers. Finally we characterize all the universal centers for the quadratic polynomial differential systems.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-00694 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-381 Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Center problem ; Universal center ; Composition conditions ; Analytic differential equations ; Polynomial differential equations ; Quadratic centers ; Iterated integrals
Published in:	Proceedings of the London Mathematical Society. Third Series, Vol. 106 (2013) , p. 481-507, ISSN 0024-6115

DOI: 10.1112/plms/pds050

Postprint 26 p, 752.3 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles