Mathematical Sciences: Classification and Automorphisms of Subshifts of Finite Type

数学科学：有限类型子移的分类和自同构

• 批准号: 9024813
• 负责人: K. Kim
• 金额: $ 7.3万
• 依托单位: Alabama State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024813&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Classification; Automorphisms; Subshifts

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.

主要研究者将研究符号动力学中与有限型子位移的拓扑分类和自同构有关的三个问题：(i)刻画了非负有理数子序列的强移位等价，（ii）开发了理解非负实数上的Williams猜想的工具，以及（iii）确定子移位的不动点的给定置换是否由自同构诱导。该奖项将支持遍历理论的一个分支——符号动力学的研究。符号动力系统是由有限字母表中两个无限的符号串组成的集合，这些符号串具有一定的形成规则，该规则规定了哪些符号可以彼此遵循。这个领域的一个中心主题是根据各种形式的等价对这些系统进行分类。符号动力系统最近在数据传输建模中得到了应用。