拓扑Markov链与混沌

The Topological Markov Chain and Chaos

本文讨论了紧致符号空间上拓扑 Markov 链的混沌性质,证明了定理:设 A 为k×k 0,1-方阵,如果 A 的有向图有一个顶点有两条不同的不可约闭路,则(∑_A,δ_A)存在不可数无穷多个彼此不相交的混沌集。

In the present paper,the following theorem is proved.Theorem :Let A=(a_ij)be a k×k 0,1—matrix and σ_A:∑_A→∑_A be the subshift determinedby A,if the directed graph A have two different irrecducible cycles through a certainvertex.Then there exists uncountable infinitely many chaotic sets of(∑_A,σ_A).which are disjoint.