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Centroaffinely invariant conditions for a Dulac center of a quadratic differential system. (English. Russian original) Zbl 0618.34027
Differ. Equations 22, 669-674 (1986); translation from Differ. Uravn. 22, No. 6, 954-961 (1986).
The author considers the system \[ (1)\quad dx^ 1/dt=a^ 1_ 1x^ 1+a^ 1_ 2x^ 2+a^ 1_{11}(x^ 1)^ 2+2a^ 1_{12}x^ 1x^ 2+a^ 1_{22}(x^ 2)^ 2, \]
\[ dx^ 2/dt=a^ 2_ 1x^ 1+a^ 2_ 2x^ 2+a^ 2_{11}(x^ 1)^ 2+2a^ 2_{12}x^ 1x^ 2+a^ 2_{22}(x^ 2)^ 2 \] with complex-valued coefficients. He derives necessary and sufficient centroaffinely invariant conditions under which the origin is a center of system (1) in the sense of H. Dulac.
Reviewer: F.Neuman

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations