关于Smale马蹄的结构稳定性讨论

Structural Stability of Smale Horseshoe

Smale马蹄(Smale Horseshoe)是S.Smale在1965年研究微分动力系统时构造出来的一个数学模型.在已有相关研究的基础上,对Smale马蹄的结构稳定性进行更深层次的分析,得到了两个重要结论:Smale马蹄在某些限制性条件下仍然成立;Smale马蹄在不变集∧上是结构稳定的.

Smale horseshoe which was constructed by S Smale under studying differentiable dynamical system in 1965 is a mathematical model. Here quoted some conclusions about Smale hor- seshoe. Carries on the deeper level discussion to the Smale horseshoe structural stability and obtain two important results： （1） the theory of Smale horseshoe still in certain restrictive conditions; （2） the Smale horseshoe is structuarally stable in the invariant series.