Universal centres and composition conditions

Jaume Giné, Maite Grau, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

30 Citations (Scopus)


In this paper, we characterize the universal centres of the ordinary differential equations, 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. © 2012 London Mathematical Society.
Original languageEnglish
Pages (from-to)481-507
JournalProceedings of the London Mathematical Society
Issue number3
Publication statusPublished - 1 Mar 2013


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