Mathematical Sciences: Topics in Symbolic Dynamics

数学科学：符号动力学主题

• 批准号: 8803260
• 负责人: Douglas Lind
• 金额: $ 4.8万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803260&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Symbolic; Dynamics

This supplementary award is to support the mathematical research of Professor Selim Tuncel on the project of the principal investigator, Professor Lind. The subject is 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 satisfying a formation rule that specifies which symbols are allowed to follow which as one moves along the string. Two such systems are equivalent if there is a well- behaved bijection between them that respects the operation of shifting. A central theme in this area is the classification of symbolic dynamical systems. Professor Tuncel will study invariants for these and related systems, including the beta function for Markov chains and an algebraic invariant resulting from dimension modules and an additional element of structure called the scaffold. Cellular automata and block codes between Bernoulli shifts are additional research topics. The mathematical structures studied in this project have found considerable use as models for communication and data systems.

这个补充奖是为了支持Selim Tuncel教授在首席研究员Lind教授的项目上的数学研究。这门学科是遍历理论的一个分支，叫做符号动力学。符号动力系统是一组来自有限字母表的双向无限符号串的集合，这些符号串满足一个形成规则，该规则规定了当一个符号沿着字符串移动时，允许哪个符号跟随哪个符号。两个这样的系统是等价的，如果它们之间有一个表现良好的双射，并尊重移位的操作。这个领域的一个中心主题是符号动力系统的分类。Tuncel教授将研究这些系统和相关系统的不变量，包括马尔可夫链的β函数，以及由维度模块和称为支架的附加结构元素产生的代数不变量。细胞自动机和块码之间的伯努利移位是额外的研究课题。在这个项目中研究的数学结构已经发现了作为通信和数据系统模型的相当大的用途。