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

Calin Iurie; Ciubotaru Stanislav

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773

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2018-10-10 08:03

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512.628+519.956 (1)

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CALIN, Iurie, CIUBOTARU, Stanislav. The Lyapunov quantities and the center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, nr. 2(84), pp. 112-130. ISSN 1024-7696.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 2(84) / 2017 / ISSN 1024-7696 /ISSNe 2587-4322

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

CZU: 512.628+519.956

MSC 2010: 34C05, 58F14

Pag. 112-130

Calin Iurie, Ciubotaru Stanislav

Institute of Mathematics and Computer Science ASM

Disponibil în IBN: 16 noiembrie 2017

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Rezumat

For the autonomous bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree the GL(2, 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,R)-invariant conditions for the existence of center are given.

Cuvinte-cheie
Polynomial differential systems, invariant, comitant, transvectant, center conditions,

Lyapunov quantities

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