Abstract |

**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