Mathematical Sciences: Topics in Symbolic Dynamics

这一补充奖是为了支持数学 塞利姆·通塞尔教授关于" 首席研究员林德教授 主题是分支 一种叫做符号动力学的遍历理论 一种象征性的动力学 系统是一个双向无限符号串的集合 从满足如下形成规则的有限字母表，该形成规则指定 当一个人沿着移动时， string. 两个这样的系统是等价的，如果有一个井- 它们之间的行为双射， 转移 这一领域的一个中心主题是 符号动力系统 Tuncel教授将研究这些和相关的不变量 系统，包括马尔可夫链的beta函数和 由维数模产生的代数不变量和一个 一种额外的结构元素叫做脚手架。蜂窝 伯努利移位之间的自动机和分组码是额外的 研究课题。本文研究的数学结构 项目已被大量用作通信模型 和数据系统。

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.