Mathematical Sciences: Classification and Automorphisms of Subshifts of Finite Type

主要研究人员将研究符号动力学中与有限型子移位的拓扑分类和自同构有关的三个问题：(I)刻画非负有理数的次半环的强移位等价；(Ii)开发工具来理解非负实数上的Williams猜想；以及(Iii)确定给定的子移位不动点的置换是否是由自同构引起的。该奖项将支持被称为符号动力学的遍历理论的一个分支的研究。符号动力系统是来自有限字母表的双向无限符号串的集合，具有指定哪些符号可以彼此跟随的构成规则。这一领域的一个中心主题是根据各种形式的等价性对这类制度进行分类。符号动力系统最近在数据传输的建模中得到了应用。

The principal investigators will study three problems in symbolic dynamics pertaining to topological classification and automorphisms of subshifts of finite type: (i) characterize strong shift equivalence for subsemirings of the nonnegative rational numbers, (ii) develop tools to understand the Williams conjecture over the nonnegative real numbers, and (iii) determine whether given permutations of the fixed points of a subshift are induced by an automorphism. This award will support research in a branch of ergodic theory called symbolic dynamics. A symbolic dynamical system is a collection of two way infinite strings of symbols from a finite alphabet with a rule of formation which specifies which symbols can follow one another. A central theme in this area is the classification of such systems with respect to various forms of equivalence. Symbolic dynamical systems have recently found application in the modelling of data transmission.