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.

首席研究者将研究有限类型的拓扑分类和自动迁移的符号动力学问题的三个问题：（i）特征是非负合理数量的实质性的强偏移等效性，（ii）开发工具以确定允许的实时数量，并确定固定的工具，并确定固定的工具，并确定固定的依据。 该奖项将支持一个名为“符号动力学”分支的研究。 符号动力系统是来自有限字母的两条无限符号字符串的集合，该字母具有形成规则，该规则指定哪些符号可以互相跟随。 该领域的一个核心主题是对各种形式的等效性进行此类系统的分类。 符号动力学系统最近在数据传输的建模中发现了应用。