A rational basis of GL (2, R )-comitants for the bidimensional polynomial system of differential equations of the fifth degree

Abstract

Definition 1. The set S of the comitants is called a rational basis on M ⊆ A of the comitants for the system with respect to the group GL(2, R) if any comitant of the system (1) with respect to the group GL(2, R) can be expressed as a rational function of elements of the set S. Definition 2. A rational basis on M ⊆ A of the comitants for the system (1) with respect to the group GL(2, R) is called minimal if by the removal from it of any comitant it ceases to be a rational basis. In [3] was established a method for construction the rational bases of GL(2, R)-comitants for the bidimensional polynomial systems of differential equations by using different comitants of the system. In this paper we will present a rational basis of GL(2, R)-comitants for the bidimensional polynomial system of differential equations of the fifth degree in the case, when the comitant of the linear part R1 ≡ 0.