摘要
对于一个混沌的区间自映射ｆ 的每个不规则集 Ｓ，相应地有一个集合 Ｖ Ｓ 与之对应．假如ｆ 的拓扑熵为零，那么对ｆ 的任意一个不规则集 Ｓ， Ｖ Ｓ 是一个可数集合；假如ｆ 的拓扑熵大于零，那么至少存在一个ｆ 的不规则集 Ｓ使得 Ｖ Ｓ
For every scrambled set S of a chaotic map f of the closed interval into itself, we associate a set V S. It is shown that if the topological entropy of f is zero, then V S is a countable set for any scrambled set S of f, and if the topological entropy of f is positive, then there exists at least a scrambled set S of f such that the V S is an uncountable set.
基金
国家自然科学基金
