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CENTER VARIETIES OF COMPLEX AND REAL TWO-DIMENSIONAL AUTONOMOUS POLYNOMIAL DIFFERENTIAL SYSTEMS

Abstract

In the present article we consider the interaction between the solution of the problem of obtaining necessary and sufficient conditions of existence of a time-independent first integral analytical in the neighborhood of the origin for the complex system of the form x = y + P(x, y), y = −x + Q(x, y), where P(x, y), Q(x, y) are polynomials without constant and linear terms, and the solution of the center-focus problem for the real system of the same form.

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ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)