The classification of $GL(2,R)$-orbits' dimensions for system $s(0,2)$ and the factorsystem $s(0,1,2)/GL(2,R)$

Two-dimensional systems of two autonomous polynomial differential equations with homogeneities of the zero, first and second orders are considered with respect to the group of center-affine transformations $GL(2,R)$. The problem of the classification of $GL(2,R)$-orbits' dimensions is solved completely for system $s(0,2)$ with the help of Lie algebra of operators corresponding to $GL(2,R)$ group, and algebras of invariants and comitants. A factorsystem $s(0,1,2)/GL(2,R)$ for system $s(0,1,2)$ is built and with its help two invariant $GL(2,R)$-integrals are obtained for the system $s(1,2)$ in some necessary conditions for the existence of singular point of the type “center”.