On a Classification of Orbits for Cubic Differential Systems

M.Popa, E.Naidenova (Academy of Sciences, Institute of Mathematics and Computer Sciences, Kishinev, Moldova)

e-mail: popam@math.md

We consider a two-dimensional system of differential equations of the first order with polynomial right . hand sides. Using the methods described in [1] the complete classification of orbits for linear representation of the group of rotations and Lorentz group in the space of coefficients of the cubic differential system is done. On the orbits of dimension zero this system has the form of a differential system with cubic nonlinearities where the right . hand sides contain four independent parameters. The first integrals and the particular invariant integrals were obtained on these orbits with respect to indicated groups. The topological classification of some of the indicated systems was considered in Poincare circle. The class of systems having a limit cycle was allocated. In the case of differential system with right-hand sides having the form of sum of homogeneities of the zero and third orders the generators of algebra of unimodular comitants were obtained and using them the classification of orbits in the space of coefficients of this system was done with respect to center-affine.  References. [1] Popa M.N. Applications of algebras to differential systems. (in Russian). Academy of Sciences of Moldova, Kishinev, 2001.


Section : 12