一类受限符号系统的拓扑熵

发布时间：2018-02-16 18:35

  本文关键词： 符号动力系统 拓扑熵 有限型子移位 长度约束　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：在拓扑动力系统领域,符号动力系统是一个重要的研究方向,其中有限型子移位在理论与应用中均具有重要意义,受到广泛关注.关于有限型子移位,现在已经有大量的研究成果,对于子移位拓扑熵的研究也是热中之重.有限长度的(d,k)约束系统被应用于各种储存系统和工业上复杂的机器运行中,定义它为一个{0,1}两个符号的约束系统,其中序列内两个相邻的“1”中间连续“0”的数量有至多d个至少k个,这样的系统已经被学者们研究,同时它也是一类空间有限型子移位,通过其特征多项式计算符号动力系统的拓扑熵,这里用C(d,k)表示拓扑熵,简单总结下来不同(d,k)约束系统的拓扑熵可以相等,这样的等式有且仅有如下形式:C(d,2d)= C(d + 1,3d + 1),C(d + 1,∞)= C(d,2d + 1),d ≥ 0,C(1,2)= C(2,4)= C(3,7)= C(4,∞).本文主要研究的是一类{0,1}两个符号的双重约束下约束系统,我们将其定义为双重约束下的(p,q)-约束系统(简记为(p,q)-DUB).这里的(p,q)约束是指{0,1}序列中的符号最多连续出现p个“0”和q个“1”,记(p,q)-DUB系统的拓扑熵为C(p,q),(d,k)约束系统拓扑熵的值可以通过相应的多项式的根得到,但是很难直接通过d,k的数值大小比较不同约束系统之间熵值的大小,但是对于(p,q)-DUB,我们找到了一个简单有效的方法很容易的比较任意两个或者多个(p,q)-约束系统的拓扑熵的大小.事实上,我们可以对所有(p,q)-约束系统的拓扑熵进行排序,结论为:0 = C(1,1) C(1,2)... C(1,∞)= C(2,2) C(2,3)... C(2,∞)=C(3,3)C(3,4)......C(∞,∞)=ln 2.值得注意的,C(p,∞)=C(p+1,p+1)是(p,q)-DUB系统的拓扑熵唯一存在的等式.
[Abstract]:In the field of topological dynamical system, symbolic dynamical system is an important research direction, in which finite type subshift is of great significance in theory and application. There have been a lot of research results, and the study of the topological entropy of subshift is also very hot. The finite length of the constrained system has been applied to various storage systems and the complex machine operation in industry. It is defined as a constraint system with two symbols {0 ~ 1}, in which the number of two adjacent "1" continuous "0" in a sequence has not more than d at least k, such a system has been studied by scholars, and it is also a class of space finite type subshifts. The topological entropy of the symbolic dynamical system is calculated by its characteristic polynomial, and the topological entropy is expressed by Cndnk), and the topological entropy of different constrained systems can be equal. This equation has the following forms, and only in the following forms: C ~ (1) C ~ (1) C ~ (1) D ~ (2) C ~ (1) C ~ (1) C ~ (1) C ~ (1), 鈭，

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