论文标题
对角图的拓扑熵在反极限空间上
Topological entropy of diagonal maps on inverse limit spaces
论文作者
论文摘要
我们就其设定值组件的拓扑距离为逆极限空间的拓扑熵提供了上限。在逆限制空间上的对角图的特殊情况下，$ \ unewerftarrow {\ lim}（i，f）$，其中每个对角线组件都是相同的映射$ g \ colon i \ to i $ to i $ to $ f $ colly $ f $（即$ f^{ - 1}} \ circ g = g = g = g = g = g \ cird fi f^civ f^$ 1} $ \ max \ {\ textrm {ent}（f），\ textrm {ent}（g）\} $。作为侧产品，我们开发了一些用于计算设定值图的拓扑熵的技术。
We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal component is the same map $g\colon I\to I$ which strongly commutes with $f$ (i.e. $f^{-1}\circ g=g\circ f^{-1}$), we show that the entropy equals $\max\{\textrm{Ent}(f),\textrm{Ent}(g)\}$. As a side product, we develop some techniques for computing topological entropy of set-valued maps.
