IMI/Publicaţii/BASM/Ediţii/BASM n.1 (29), 1999/

Solution of the problem of the center for cubic system with two homogeneous and one nonhomogeneous invariant straight lines. (English)

Authors: Şubă Alexandru, Cozma D.


It is proven that the cubic differential system $\dot x=y+P_2(x,y)+P_3(x,y)$, \linebreak $\dot y=-(x+Q_2(x,y)+Q_3(x,y))$, where $P_i$, $Q_i$ are homogeneous polynomials of degree $i$ with the invariant straight lines $x\pm iy=0$, $1+Ax+By=0,$ has a center at the origin if and only if the focal values $g_{2j+1}$, $j=\overline{1,\,7},$ vanish.

State University of Moldova
str. A.Mateevici, 60, MD-2009 Chisinau, Moldova
Tiraspol State University
str. Gh.Iablocichin, 5, MD-2069 Chisinau, Moldova