摘要
本文研究了一类定义在二维空间R^2上C^r收缩面积的单参数微分同胚族f_t,t∈R,r>2。指出当稳定流形与不稳定流形非退化相切时会出现马蹄形不变集,从而证明参数t变化时,分歧反复出现,因此存在无穷多周期倍增的吸引周期轨道。本文的结果加强了Silnikov等人的有关结论。
In this paper, one-parameter family of C^r maps f_t for t∈R, r>2 in two dimensions is investigated. It is proved that if the stable and unstable manifolds of f_t have a nondegenerately homoclinic tangency as the parameter t varies, the horseshoes invariant set is created and there are infinitely period doubling attracting periodic orbits. The conclusion of this paper is stronger than that of Silnikov's.
关键词
周期倍增分歧
映射族
分歧过程
period doubling bifurcation
homoclinic intersection
invariant set
