Topological entropy on closed sets in [0,1] 2
Topological entropy on closed sets in [0,1] 2
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[0,1] 2 内闭集上的拓扑熵
DOI：
10.1016/j.topol.2018.06.015
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发表时间：
2017
影响因子：
0.6
通讯作者：
J. Kennedy
中科院分区：
文献类型：
--
作者：
G. Erceg;J. Kennedy
我们将Adler， Konheim， and McAndrew[1]给出的拓扑熵的定义推广到集值函数，从区间的闭子集a到区间的闭子集。我们把这些集值函数，通过它们的图，看作[0,1]2的封闭子集。我们证明了紧致拓扑空间的连续函数的许多拓扑熵性质在我们的新设置中是成立的，但不是全部。我们还计算了一些示例的拓扑熵，将熵与示例的其他动态和拓扑性质联系起来，并给出了一个闭合子集G（[0,1] 2）的熵为0但G∪{(p, q)}的例子，其中(p, q)∈[0,1]2∈G具有无限熵。
We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew [1] to set-valued functions from a closed subset A of the interval to closed subsets of the interval. We view these set-valued functions, via their graphs, as closed subsets of [0, 1] 2. We show that many of the topological entropy properties of continuous functions of a compact topological space to itself hold in our new setting, but not all. We also compute the topological entropy of some examples, relate the entropy to other dynamical and topological properties of the examples, and we give an example of a closed subset G of [0, 1] 2 that has 0 entropy but G∪{(p, q)}, where (p, q)∈[0, 1] 2∖ G, has infinite entropy.