The set of sequence entropies for a given space
The set of sequence entropies for a given space
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DOI：
10.1088/0951-7715/23/1/009
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发表时间：
2009
期刊：
影响因子：
1.7
通讯作者：
Feng Tan;X. Ye;Ruifeng Zhang
中科院分区：
文献类型：
--
作者：
Feng Tan;X. Ye;Ruifeng Zhang
设X是紧度量空间，T：X → X是连续的.设h*（T）是T在X上的所有连续映射上的序列熵的上确界，S（X）是X上所有连续映射T的h*（T）的集合.已知S（X）<${∞，0，log 2，log 3，.}。本文证明了：若X是有限树或单位圈S_1，则S（X）= {∞，0，log 2}.进一步证明了若X = [0，1]且T的拓扑熵为零，则序列熵偶的集合是可数的，且任一序列熵偶都是渐近的.确定了零维空间X中S（X）的所有可能集合。此外，还证明了对每个连续统，存在一个n维连续统Xn，使得S（Xn）= {∞，0，log 2，log 3，.}.
Let X be a compact metric space and T : X → X be continuous. Let h*(T) be the supremum of sequence entropies of T over all subsequences of and S(X) be the set of h*(T) for all continuous maps T on X. It is known that S(X) ⊏ {∞, 0, log 2, log 3, …}. In this paper it is proved that if X is a finite tree or the unit circle S1 then S(X) = {∞, 0, log 2}. Moreover, it is shown that if X = [0, 1] and T has zero topological entropy then the set of sequence entropy pairs is countable and any sequence entropy pair is asymptotic. All the possible sets of S(X) for zero-dimensional spaces X are determined. Moreover, it is shown that for each there is a continuum Xn with dimension n such that S(Xn) = {∞, 0, log 2, log 3, …}.