Universal centres and composition conditions

Jaume Giné; Maite Grau; Jaume Llibre

doi:10.1112/plms/pds050

Universal centres and composition conditions

Jaume Giné, Maite Grau, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

27 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	481-507
Journal	Proceedings of the London Mathematical Society
Volume	106
Issue number	3
DOIs	https://doi.org/10.1112/plms/pds050
Publication status	Published - 1 Mar 2013

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AB - 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.

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