Center problem in the center manifold for quadratic differential systems in R^3
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Using tools of computer algebra based on the Gröbner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen seven-parameter families of quadratic systems on R 3. To obtain the results we use modular arithmetics.
Is part ofJournal of Symbolic Computation, 2016, vol. 73, p. 250-267
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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 ...
Giné, Jaume; Llibre, Jaume; Valls, Claudia (Texas State University, 2019)We characterize the centers of the Chiellini Hamiltonian Li´enard second-order differential equations x 0 = y, y 0 = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α) R f(x)dx) with α, k ∈ R. Moreover we study the ...
Giné, Jaume; Valls, Claudia (Elsevier, 2017)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 ...