Browsing by Author "Ciubotaru, Stanislav"

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THE LYAPUNOV QUANTITIES AND THE GL(2,R)-INVARIANT CENTER CONDITIONS FOR A CLASS OF BIDIMENSIONAL POLYNOMIAL SYSTEMS OF DIFFERENTIAL EQUATIONS WITH NONLINEARITIES OF THE FOURTH DEGREE
(CEP USM, 2017) Ciubotaru, Stanislav; Calin, Iurie
For the bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree the recurent equations for determination of the Lyapunov quantities were established. Moreover, the general form of Lyapunov quantities for the mentioned systems were obtained. For a class of such systems the necessary and sufficient GL(2,R)-invariant conditions for the existence of center are given.
THE RATIONAL BASES OF GL(2;R)-COMITANTS AND OF INVARIANTS FOR THE BIDIMENSIONAL SYSTEM OF DIFFERENTIAL EQUATIONS WITH NONLINEARITIES OF THE FOURTH DEGREE
(Valines SRL, 2014) Calin, Iurie; Ciubotaru, Stanislav
In this paper minimal rational bases of GL(2;R)-comitants and a rational basis of GL(2;R)-invariants for the bidimensional system of differential equations with nonlinearities of the fourth degree are presented.