THE CENTER CONDITIONS FOR A CLASS OF CUBIC SYSTEMS

Abstract

One of famous problems of the theory of Differential equations, namely, center-focus problem, are considered. For the cubic vector field

\[
i\frac{dw}{dt}
=
w\left(
1-a_{10}w-a_{01}\overline{w}
-a_{11}w\overline{w}
-a_{-13}w^{-1}\overline{w}^{3}
\right),
\]

in the case when \(a_{11}\ne -a_{10}a_{01}\) the necessary and some sufficient center conditions are obtained.