Mathematical Sciences: Classification and Automorphisms of Subshifts of Finite Type

主要研究人员将研究三个问题， 符号动力学属于拓扑分类， 有限型子移位的自同构：（i）刻画强 非负有理子半环的移位等价 数字，（ii）开发工具来理解威廉姆斯猜想 在非负真实的数上，以及（iii）确定是否 子移位的不动点的给定置换由以下导出： 自同构 该奖项将支持遍历理论分支的研究 叫做符号动力学。 符号动力系统是一个 一个有限符号的双向无限符号串的集合 一种字母表，其形成规则规定了哪些符号可以 彼此追随。 这一领域的一个中心主题是 这些系统的分类，相对于各种形式的 等价性 符号动力系统最近发现 在数据传输建模中的应用。

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.