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- Title
CENTER CONDITIONS FOR GENERALIZED POLYNOMIAL KUKLES SYSTEMS.
- Authors
GINÉ, JAUME
- Abstract
In this paper we study the center problem for certain generalized Kukles systems x = y, y = P0(x) + P1(x)y + P2(x)y2 + P3(x)y3, where Pi(x) are polynomials of degree n, P0(0) = 0 and P'0(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.
- Subjects
POLYNOMIALS; ARITHMETIC; DIFFERENTIAL equations; LYAPUNOV functions; MATHEMATICS theorems; EXTERIOR differential systems
- Publication
Communications on Pure & Applied Analysis, 2017, Vol 16, Issue 2, p417
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2017021