Nondegenerate centers for Abel polynomial differential equations of second kind
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In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems for lower degrees.
Is part ofJournal of Computational and Applied Mathematics, 2017, vol. 321, p. 469-477
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Giné, Jaume; Llibre, Jaume; Valls, Claudia (Shanghai Normal University & Wilmington Scientific Publisher, 2017)For the polynomial differential system x˙=−y, y˙=x+Qn(x,y), where Qn(x,y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for n≥2 has a ...
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Giné, Jaume (Texas State University, 2017)In this article we study the center problem for polynomial BiLiénard systems of degree n. Computing the focal values and using Gröbner bases we end the center conditions for such systems for n = 6. We also establish ...