有限子移位混沌性质的若干研究

Chaotic Behaviors in Finite Subshifts

用有向图描述有限于移位，给出了有限子移位为拓扑混合的充要条件。在此基础上，利用非负方阵的置换标准形证明了谱分解定理。重新考察了二次映射双曲不变集的存在性，并对现有论证作了若干补充。

A necessary and sufficient condition is given for topologically mixed finite subshifts that are described by directed graphs. Based on this result, the spectral decomposition theorems are proved by using permutation canonical forms of nonnegative matrices. The existence of hyperbolic invariant set possessed by the quadratic map is re-examined. Some details missed in the references are provided and a new type of finite subshifts is found.