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IMCS/Publications/BASM/Issues/BASM n.2(90), 2019/

Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems.

Authors: Calin Iurie, Baltag Valeriu

Abstract

The autonomous two-dimensional polynomial cubic systems of differential equations with pure imaginary eigenvalues of the Jacobian matrix at the singular point (0,0) are considered in this paper. The center problem was studied for three classes of such systems: the class of cubic systems with zero divergence of the cubic homogeneities (S 3 ≡ 0), the class of cubic systems with zero divergence of the quadratic homogeneities (S2 ≡ 0) and the class of cubic systems with nonzero divergence of the quadratic homogeneities (S2≢0). For these systems, sufficient GL(2,R)-invariant center conditions for the origin of coordinates of the phase plane were established.

Iurie Calin
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
& Moldova State University,
Chisinau, Republic of Moldova
E-mail:

Valeriu Baltag
Vladimir Andrunachievici Institute of
Mathematics and Computer Science
E-mail:

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