The sufficient 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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CALIN, Iurie, CIUBOTARU, Stanislav. The sufficient center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 29-30. ISBN 978-9975-76-247-2.

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Conference on Applied and Industrial Mathematics
Ediţia a 26-a, 2018

Conferința "Conference on Applied and Industrial Mathematics"
Iași, România, Romania, 20-22 septembrie 2018

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

Pag. 29-30

Calin Iurie¹, Ciubotaru Stanislav²

¹ Vladimir Andrunachievici Institute of Mathematics and Computer Science,
² Moldova State University

Proiecte:

Menționat în lucrare: 15.817.02.03F Invarianți algebrici și geometrici în studiul calitativ al sistemelor diferenţiale polinomiale

Disponibil în IBN: 31 mai 2022

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Let us consider the system of di_erential equations with nonlinearities of the fourth degree where Pi(x; y) and Qi(x; y) are homogeneous polynomials of degree i in x and y with real coe_- cients. We shall consider the following polynomials. which in fact are GL(2;R)-comitants [1, 2] of the _rst degree with respect to the coe_cients of system (1). Let us consider the following GL(2;R)-comitants and GL(2;R)-invariants for the system (1), constructed by using the comitants Ri and Si (i = 1; 4) and the notion of the transvectant [3] (in the list below, the bracket "[[" is used in order to avoid placing the otherwise necessary parenthesis .