关于拓扑强混合及初值敏感依赖

On topological strong mixing and sensitive dependence on initial conditions

考虑f为紧致度量空间(X,d)到自身的连续映射,-f:K(X)→K(X)为f诱导的集值映射,其中K(X)为X的所有非空紧子集赋予由d诱导的Hausdorff度量所得空间,Ω为K(X)的特殊子空间.研究了f与fN、f与f×N以及f与-f|Ω的拓扑强混合、初值敏感依赖之间的关系.

It is considered that the continuous map f： X→X and the induced map f： K （X）→K （X）, where X is a compact metric space and K（X） is the space of all non-empty compact subsets of X endowed with the Hausdorff metric H,Ω is a special subspace of K（X）. The relationship between f and f^N,f and f^xN as well as f and f ｜Ω regarding topological strong mixing and sensitive dependence on initial conditions are investigated.