广义符号动力系统中的Li-Yorke混沌集和ω-混沌集

Li-Yorke Chaotic Set and ω-Chaotic Set of the Generalized Symbolic Dynamical Systems

本文在广义符号动力系统Σ(Z^+)中构造一个传递的、不变的、不可数的Li-Yorke混沌集,且这个混沌集D(?)Σ(Z^+)\(?)Σ(N),还构造了一个不可数的ω-混沌集,且这个混沌集S'(?)Σ(Z^+)\(?)Σ(N)。说明了广义符号动力系统的混沌性状不是集中在有限个符号的动力系统中,在有限个符号动系统(?)Σ(N)的外部仍然具有较强的混沌性状。

In this article, a LbYorke chaotic set, that is transitive, invariant and uncountable, is constructed in the generalized symbolic dynamical system Σ（Z） and the chaotic set D（C）Σ（Z＋）／∞∪N=2Σ（N） is further proved. Moreover a co-chaotic set is then constructed and the chaotic set S＇（C）Σ（Z＋）／∞∪N=2Σ（N）. is also proved. It shows that the chaotic properties of generalized symbolic dynamical system do not focus on the symbolic dynamical system in which the number of symbolic is limited. It has very strong chaotic property outside the symbolic dynamical system with limited number of symbolic ∞∪ N=2Σ（N）