In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we...In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we prove that 5 - 4 distribution of critical points for cubic system is impossible by using the method of basic triangle and index formula. Then we discuss the possible distributions of cubic systems with eight, seven or six finite critical points.展开更多
文摘In [1]-[3], the Berlinskii's theorem of the distribution of critical points for quadratic differential systems is extended to the general n-th differential systems with n2 finite critical points. In this paper, we prove that 5 - 4 distribution of critical points for cubic system is impossible by using the method of basic triangle and index formula. Then we discuss the possible distributions of cubic systems with eight, seven or six finite critical points.
