平面有界三次系统有限奇点分布举例

摘要

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.%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11种类型；(3)赤道附近轨线拓扑结构相同的有界三次系统它们有限奇点的分布可以有不同类型。