超空间上的诱导映射的极限行为(英文)

Limit behaviors on the induced maps of hyperspaces

设（X，f）为一个动力系统．X的超空间是指由X的所有非空闭子集构成的集簇并赋予Vietories拓朴，它对于联系一维系统和高维流形具有很重要的作用．本文主要研究了f，f，f之间的一些极限行为，如：distal性质、proximal性质和扩张性质；同时证明了等度连续性（一致刚性）在f，f，f之间的等价性.

Let （X,f） be a dynamical system. The hyperspace of X is a specified collection of non-empty closed subsets of X with the Vietoris topology,which is very important for connecting one-dimension manifolds with high-dimension manifolds. In this paper,the relationship of some limit behaviors such as distality,proximity,expansivity among f, f,and f is studied. The equivalence of equicontinuity （uniform rigidity respectively） among f,f,and f is also proved.