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On general algebraic mechanisms for producing centers in polynomial differential systems

Authors:

Institution:

(1) School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon, PL4 8AA, UK;(2) Département de Mathématiques et de Statistique, Université de Montréal, C.P. 6128 Succursale Centre-Ville, Montréal, Québec, H3C 3J7, Canada

Abstract:

We classify nondegenerate centers of systems of the form

$\dot{x} = P_{3}(x)y,{\quad}\dot{y} = P_{0}(x) + P_{1}(x)y + P_{2}(x)y^{2}$

, where the P _i(x) are polynomials in x, y over ${{\mathbb{R}}}$ . We show that such systems fall naturally into two classes: those with Darboux first integrals, and those which arise from simpler systems via singular algebraic transformations. Dedicated to V. I. Arnold on his 70th birthday

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 34C20 34C25 34C14 34C07

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