论文标题
非自主系统的班次限制
Shift limits of a non-autonomous system
论文作者
论文摘要
令$ t = t_1t_2 \ cdots $是一组有限字符$ \ mathcal {a} $的移位映射$τ$的完整移位元素，让$σ= \ text {clote} \ clote} \ {τ^i（t）：\;令$ f_t = f_ {t_1，\，\，\ infty} = \ cdots \ circ f_ {t_2} \ circ f_ {t_1} $在紧凑型公制$ x $上是一个非自主系统，其中$ x $ where $ t_i \ in \ nathcal in \ nathcal a $。集合$ \ f_t^+= \ {f_ {τ^i（t）}：\; i \ in \ n \} $称为$ f_t $的移位族。如果$ t $是$ \ mathcal a $的全部变化的及传递点，那么通过引入自然拓扑，$ \ overline {\ f_t^+} $是经典的ifs;否则，$ \+edline {\ f_t^+} = \ {f_σ= f_ {σ_1，\，\ infty}：\; σ\inς\} $是概括的IF。我们将证明，如果$ f_t $具有一些各种阴影和规范属性，那么对于$f_σ\ in \ overline {\ f^+_ t} $是正确的；但是，对于其他特性，例如传递性，混合和精确性，这种说法并不正确。另外，如果$σ$是sofic，而x $ in x $的$ x \对于某些$f_σ\ in \ coperline {\ f^+_ t} $的定期点，那么有一个定期的$σ'\inς$，因此$ x $是$ f_ {σ'} \ in \ in \ overline \ overline oflline for $ f_ f_ forlline for $ x $。
Let $t=t_1t_2\cdots$ be an element of the full shift with shift map $τ$ on a finite set of characters $\mathcal{A}$ and let $ Σ=\text{ closure} \{τ^i(t):\;i\in\N\cup\{0\}\}$. Let $f_t=f_{t_1,\,\infty}=\cdots\circ f_{t_2}\circ f_{t_1} $ be a non-autonomous system over a compact metric space $ X $ where $t_i\in \mathcal A $. The set $\F_t^+=\{f_{τ^i(t)}:\; i\in\N\}$ is called the shifted family of $f_t$. If $t$ is a transitive point of the full shift on $\mathcal A$, then by introducing a natural topology, $\overline{\F_t^+}$ is a classical IFS; otherwise, $\overline{\F_t^+}=\{f_σ=f_{σ_1,\,\infty}:\; σ\inΣ\}$ is a generalized IFS. We will show that if $ f_t$ has some various shadowing and specification properties, then this is true for $f_σ\in\overline{\F^+_t}$; however, this claim is not true for other properties such as transitivity, mixing and exactness. Also, if $ Σ$ is sofic and $x\in X$ is periodic point for some $f_σ\in\overline{\F^+_t}$, then there is a periodic $σ'\inΣ$ such that $x$ is periodic for $f_{σ'}\in\overline{\F^+_t}$.
