首先证明: 若区间映射$f$是敏感依赖的, 则$f$的拓扑熵$\mathrm{e}\mathrm{n}\mathrm{t}(f)>0$. 然后通过引入一种扩张映射进一步证明了敏感依赖的区间映射的拓扑熵的下确界为0, 即, 上式中拓扑熵的下界0是最优的.最后通过实例展示稠混沌、Spatio-temporal混沌、Li-Yorke敏感及敏感性之间是几乎互不蕴含的.

In this paper, it is first proved that the topological entropy of f is positive provided that f is sensitive interval map. Then, by introducing of a kind of extended mappings, it is proved that the infimum of topological entropy of sensitive interval mappings is 0, which shows that the lower bound 0 of the topological entropy is optimal. Finally, some examples are given to show that dense chaos, Spatio-temporal chaos, Li-Yorke sensitivity and sensitivity are almost all independent.