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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017 Number 2, Pages 112–130 (Mi basm450)

This article is cited in 1 paper

Research articles

The Lyapunov quantities and the center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree

Iurie Calina, Stanislav Ciubotarub

a Institute of Mathematics and Computer Science Academy of Sciences of Moldova, Chişinău, Moldova
b Moldova State University, Chişinău, Moldova

Abstract: For the autonomous bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree the $GL(2,\mathbb R)$-invariant recurrence equations for determination of the Lyapunov quantities were established. Moreover, the general form of Lyapunov quantities for the mentioned systems is obtained. For a class of such systems the necessary and sufficient $GL(2,\mathbb R)$-invariant conditions for the existence of center are given.

Keywords and phrases: polynomial differential systems, invariant, comitant, transvectant, Lyapunov quantities, center conditions.

MSC: 34C05, 58F14

Received: 07.11.2016

Language: English



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