Invariant conditions for the dimensions of the $GL(2,R)$-orbits for one differential cubic system

A two-dimensional system of two autonomous polynomial equations with homogeneities of the zero and third orders is considered concerning to the group of center-affine transformations $GL(2,R)$. The problem of the classification of $GL(2,R)$-orbit's dimensions is solved completely for the given system with the help of Lie algebra of operators corresponding to the $GL(2,R)$ group, and algebra of invariants and comitants for the indicated system is built. The theorem on invariant division of all coefficient's set of the considered system to nonintersecting $GL(2,R)$-invariant sets is obtained.