## Centroaffine comitants of a quadratic-cubic two-dimensional differential system.(Russian)Zbl 0586.34042

Consider the system (*) $$dx^ j/dt=a^ j_{\alpha \beta}x^{\alpha}x^{\beta}+a^ j_{\alpha \beta \gamma}x^{\alpha}x^{\beta}x^{\gamma}$$ $$(j,\alpha,\beta,\gamma =1,2)$$, where $$a^ j_{\alpha \beta}$$ and $$a^ j_{\alpha \beta \gamma}$$ are symmetric tensors with respect to $$\alpha$$,$$\beta$$,$$\gamma$$. A centroaffine comitant for (*) is of the type $$(q,h_ 1,h_ 2)$$, if there exists a homogeneous polynomial of degree $$q,h_ 1,h_ 2$$ with respect to the coordinates of $$x^{\delta}$$, $$a^ j_{\alpha \beta}$$, $$a^ j_{\alpha \beta \gamma}$$ respectively. The number $$h=h_ 1+h_ 2$$ is called the order of such a comitant. It is known that the minimal polynomial basis of comitants for a homogeneous quadratic and for a homogeneous cubic system contains eight invariants and twenty comitants of order $$k\leq 4$$. This paper is devoted to the construction of a minimal polynomial basis of comitants and of invariants for (*) up to fourth order.
Reviewer: P.Talpalaru

### MSC:

 37-XX Dynamical systems and ergodic theory
Full Text: