On Berlinskii's theorem for cubic systems (Q2748234)

Here, Berlinskii's theorem on the distribution of critical points for quadratic differential systems is extended to general differential systems with \(n^{2}\) finite critical points. Using the basic triangle method and the index formula, the author proves that the \((5,4)\)-distribution of critical points is impossible for cubic systems and discusses possible distributions of eight, seven and six finite critical points in this case.