论文标题
在任意偏移空间上的迭代功能系统
Iterated function systems over arbitrary shift spaces
论文作者
论文摘要
经典迭代功能系统（IFS）中x $的点$ x \的轨道可以定义为$ \ {f_u（x）= f_ {u_n} \ circ \ circ \ circ \ circ f_ {u_1}（u_1}（x）（x）：$ u_1 \ u_1 \ cdots u_n $是$ x $ $ \} $上的连续自我地图。 One also can associate to $σ=σ_1σ_2\cdots\inΣ$ a non-autonomous system $(X,\,f_σ)$ where the trajectory of $x\in X$ is defined as $x,\,f_{σ_1}(x),\,f_{σ_1σ_2}(x),\ldots$.Here instead of the full shift, we考虑一个任意的换档空间$σ$。然后，我们研究了与此IFS和相关的非自主系统有关的基本属性。特别是，我们寻找足够的条件，可以保证在及时的IF中，对于某些$σ\inς$，可能具有传递性$（x，\，f_σ）$，以及如此丰富的$σ$。
The orbit of a point $x\in X$ in a classical iterated function system (IFS) can be defined as $\{f_u(x)=f_{u_n}\circ\cdots \circ f_{u_1}(x):$ $u=u_1\cdots u_n$ is a word of a full shift $Σ$ on finite symbols and $f_{u_i}$ is a continuous self map on $X$ $\}$. One also can associate to $σ=σ_1σ_2\cdots\inΣ$ a non-autonomous system $(X,\,f_σ)$ where the trajectory of $x\in X$ is defined as $x,\,f_{σ_1}(x),\,f_{σ_1σ_2}(x),\ldots$.Here instead of the full shift, we consider an arbitrary shift space $Σ$. Then we investigate basic properties related to this IFS and the associated non-autonomous systems. In particular, we look for sufficient conditions that guarantees that in a transitive IFS one may have a transitive $(X,\,f_σ)$ for some $σ\inΣ$ and how abundance are such $σ$'s.
