THE ????????(????, ℝ)-COMITANTS FOR THE HOMOGENEOUS BIDIMENSIONAL POLYNOMIAL SYSTEM OF DIFFERENTIAL EQUATIONS OF THE FOURTH DEGREE

Stanislav CIUBOTARU Institutul de Matematică și Informatică

Abstract

For the homogeneous bidimensional polynomial system of differential equations of the fourth degree, the types, subtypes and the number of irreducible ????????(2, ℝ)-comitants and ????????(2, ℝ)-invariants up to the eighteen degree including were determined. A minimal polynomial bases of ????????(2, ℝ)-comitants and of ????????(2, ℝ)-invariants up to eighteen degree including were constructed for the mentioned system. Keywords: polynomial systems of differential equations, comitants, invariants, transvectants, minimal polynomial basis.