×

zbMATH — the first resource for mathematics

Center conditions for a polynomial differential system. (English) Zbl 1275.34047
Differ. Equ. 49, No. 2, 151-165 (2013); translation from Differ. Uravn. 49, No. 2, 151-164 (2013).
The authors obtain 16 center conditions for a polynomial differential system with 27 parameters.

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Sadovskii, AP; Shcheglova, TV, Solution of the center-focus problem for a cubic system with parameters, Differ. Uravn., 47, 209-224, (2011)
[2] Sadovskii, AP; Shcheglova, TV, Centers of a cubic system with eleven parameters, 71-75, (2011) · Zbl 1247.34046
[3] Romanovski, V.G. and Shafer, D.S, The Center and Cyclity Problems: A Computational Algebra Approach, Boston, 2009.
[4] Sadovskii, A.P., Polinomial’nye idealy i mnogoobraziya (Polynomial Ideals and Manifolds), Minsk, 2008.
[5] Cherkas, LA, Conditions for a center for a certain lienard equation, Differ. Uravn., 12, 292-298, (1976) · Zbl 0328.34023
[6] Cherkas, LA, Conditions for a center for the equation yy′ = ∑_{\(i\)=0}\^{}{3}\(P\)_{i}(\(x\))\(y\)\^{}{i}, Differ. Uravn., 14, 1594-1600, (1978) · Zbl 0414.34045
[7] Sadovskii, AP, On conditions for center and focus for nonlinear oscillation equations, Differ. Uravn., 15, 1716-1719, (1979)
[8] Amel’kin, V.V., Lukashevich, N.A., and Sadovskii, A.P., Nelineinye kolebaniya v sistemakh vtorogo poryadka (Nonlinear Oscillations in Second-Order Systems), Minsk: Belarus Gos. Univ., 1982.
[9] Sadovskii, AP, Lyurot theorem and cherkas method, Tr. 5-i mezhdunar. konf. “Analiticheskie metody analiza i differentsial’nykh uravnenii”, 2, 120-122, (2010)
[10] Van der Waerden, B.L., Algebra (Algebra), Moscow, 1976. · Zbl 0997.00501
[11] Cox, D., Little, J., and O’Shea, D., Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, New York: Springer Verlag, 1997. Translated under the title Idealy, mnogoobraziya i algoritmy. Vvedenie v vychislitel’nye aspekty algebraicheskoi geometrii i kommutativnoi algebry, Moscow, 2000.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.