Analytic reducibility of nondegenerate centers: Cherkas systems
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In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials of degree n, P0(0)=0 and P′0(0)<0. Computing the focal values we find the center conditions for such systems for degree 3, and using modular arithmetics for degree 4. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree n.
Is part ofElectronic Journal of Qualitative Theory of Differential Equations, 2016, núm. 49, p. 1–10
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Except where otherwise noted, this item's license is described as cc-by (c) Giné, Jaume et al., 2016
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