Note on a theorem of Berlinskiĭ

Andr{és Sestier
1980 Proceedings of the American Mathematical Society  
If a quadratic differential system has four singular points, these are elementary and the sum of their indices is 0 iff the quadrilateral with vertices at the singular points is convex; otherwise the sum of indices is 2 or -2. These facts and the relative positions of the two kinds of singular points are readily proved by consideration of the pencil of isoclines of the system. The theorem is originally due to Berlinskii.
doi:10.1090/s0002-9939-1980-0553376-6 fatcat:f7ziquzwjzgbdbswmxnqsk2kvy