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On entropy and intrinsic ergodicity of coded subshifts
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-08-05 , DOI: 10.1090/proc/15145 Ronnie Pavlov
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-08-05 , DOI: 10.1090/proc/15145 Ronnie Pavlov
Abstract:Any coded subshift 
defined by a set 
of code words contains a subshift, which we call 
, consisting of limits of single code words. We show that when 
satisfies the unique decipherability property, the topological entropy 
of 
is determined completely by 
and the number of code words of each length. More specifically, we show that 
exactly when a certain infinite series is less than or equal to 
, and when that series is greater than 
, we give a formula for 
. In the latter case, an immediate corollary (using a result from [Israel J. Math. 192 (2012), pp. 785-817] is that 
has a unique measure of maximal entropy.
中文翻译：
编码子移位的熵和内在遍历性
摘要：由一组代码字定义的任何编码子移位都包含一个子移位，我们称此子移位为单个代码字的限制。我们表明，当满足唯一可译码性能，拓扑熵的完全由确定和各自的长度的码字的数目。更具体地说，我们证明了当某个无限级数小于或等于时，以及当该级数大于时，我们给出的公式。在后一种情况下，直接推论（使用来自[Israel J. Math。192（2012），第785-817页的结果]）具有唯一的最大熵度量。
更新日期：2020-09-02
defined by a set of code words contains a subshift, which we call , consisting of limits of single code words. We show that when satisfies the unique decipherability property, the topological entropy of is determined completely by and the number of code words of each length. More specifically, we show that exactly when a certain infinite series is less than or equal to , and when that series is greater than , we give a formula for . In the latter case, an immediate corollary (using a result from [Israel J. Math. 192 (2012), pp. 785-817] is that has a unique measure of maximal entropy. 中文翻译：
编码子移位的熵和内在遍历性
摘要：
由一组代码字定义的任何编码子移位都包含一个子移位，我们称此子移位为单个代码字的限制。我们表明，当满足唯一可译码性能，拓扑熵的完全由确定和各自的长度的码字的数目。更具体地说，我们证明了当某个无限级数小于或等于时，以及当该级数大于时，我们给出的公式。在后一种情况下，直接推论（使用来自[Israel J. Math。192（2012），第785-817页的结果]）具有唯一的最大熵度量。 
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