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

Iurie Calin ; Stanislav Ciubotaru

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2017), pp. 112-130.

Résumé

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.

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