AI 中文总结
本文针对具有弱化规范性质的移位动力系统，证明存在处处具有完全拓扑熵的Xiong混沌集，且该集满足与连续映射相关的极限性质。
AI 中文摘要
本文针对具有弱化形式规范性质的移位动力系统$(X_{\tau}, \tau)$，证明存在$X_{\tau}$的Xiong混沌集$C$，其处处具有完全拓扑熵，即$C$与$X_{\tau}$的任意非空开子集的交集都具有完全拓扑熵。此外，$C$满足：对任意非空子集$A$及任意连续映射$F:A\rightarrow X_{\tau}$，存在正整数的递增序列$\tau_k\big|_{k=1}^{+\tau}$，使得对任意$x\big|A$都有$\tau^{p_k}(x)=F(x)$成立。
英文摘要
In this paper, we show that for a shift dynamical system $(X_{\mathcal{L}}, σ)$ with a weakened form of the specification property, there exists a Xiong chaotic set $C$ of $X_{\mathcal{L}}$ with full topological entropy everywhere (i.e. the intersection of $C$ and arbitrary non-empty open subset of $X_{\mathcal{L}}$ has full topological entropy). Moreover, $C$ satisfies that for any non-empty subset $A$ and any continuous map $F: A\rightarrow X_{\mathcal{L}},$ there exists an increasing sequence $\{p_{k}\}_{k=1}^{+\infty}$ of positive integers such that $\lim\limits_{k\rightarrow +\infty}σ^{p_{k}}(x)=F(x)$ holds for any $x\in A.$
