平面有界三次系统有限奇点分布举例

On the distribution of finity critical points of bounded cubic systems in the plane

通过构造有界的平面三次系统 ,证实了 (1 )其有限奇点的 5- 4(5个奇点指标为 +1 ,另 4个奇点指标为 - 1 )、3- 2、2 - 1、+1四种分布均可实现 ;(2 )仅有一个指标为 +1的有限奇点的有界三次系统至少有 1 1种类型 ;(3)

By structure the bounded cubic systems in the plane,we prove that:1) the system (1) have distribution of critical point with 5-4 (5 critical points with index +1 and 4 critical points with index -1),3-2,2-1,+1;2) the bounded cubic systems in the plane which has only one critical point with index +1 have at least 11 structures;3) the distribution of finity critical points of bounded cubic systems with same topological structure near the equator have different struction.