Cubic Systems with Invariant Straight Lines of Total Multiplicity Eight and with Three Distinct Infinite Singularities

Center Problem for Cubic Differential Systems With the Line at Infinity and an Affine Real Invariant Straight Line of Total Multiplicity Four

“…The cubic systems (1) with invariant straight lines were investigated in the works [2,3,4,10,11,13,14,15,16,26,27,28,29,30],…”

“…(5a 2 + 4(2 + c) 2 )f3 If f 1 = 0, thenLemma 7, (vi), and if f 2 = f 3 = 0, i.e. g = −1, c = −3/2, then Lemma 8.…”

“…We express c from L 1 = 0 : c = −B c /A c and replacing in L j , j = 2, 3, 4, we obtain L 2 = F 1 F 2 F 3 (see ( 14)), where 3 ), and L j = F 1 F 2 F j+1 , j = 3, 4. The polynomials F 4 , F 5 (in a, b, f ) are very large and they are not given here.…”