Two-dimensional homogeneous cubic systems: classification and normal forms — II

Abstract

In the first part of the paper properly designed structural principles are given to introduce a total order on the set of structural forms — vector polynomials with a fixed number of zero coefficients which represent right-hand parts of two-dimensional homogeneous cubic systems of ODE. Among them normalized based on the principles of normalization structural forms and linear non-equivalent to each other, the simplest in their class canonical forms (CF) are sequentially distinguished. In the second part of the paper for the mentioned systems the right-hand part components of which are proportional all CF are distinguished with their canonical sets of permissible values. For each CF are given: a) the conditions on the coefficients of the original system, b) linear substitutions that reduce the right-hand part of the system under these conditions to the chosen CF, c) obtained values of CF’s coefficients. This paper is a direct continuation of [1], so it retains all previously introduced notations. Refs 1.