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Center conditions for generalized polynomial kukles systems

The author is partially supported by a MINECO/FEDER grant number MTM2014-53703-P and by a AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204
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  • Abstract. In this paper we study the center problem for certain generalized Kukles systems $\dot{x}= y, \qquad \dot{y}= P_0(x)+ P_1(x)y+P_2(x) y^2+ P_3(x) y^3, $ where Pi(x) are polynomials of degree n, P0(0) = 0 and P0′(0) < 0. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems when P0 is of degree 2 and Pi for i = 1; 2; 3 are of degree 3 without constant terms. We also establish a conjecture about the center conditions for such systems.

    Mathematics Subject Classification: Primary: 34C05; Secondary: 37C10, 34C25, 34C07.


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