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IMI/Publicaţii/BASM/Ediţii/BASM n.2(84), 2017/

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

Authors: Calin Iurie, Ciubotaru Stanislav

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.

Iurie Calin
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova &
Moldova State University, Chisinau
Moldova
E-mail:

Stanislav Ciubotaru
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
E-mail:

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