Mathematical Sciences: Stable Classification and Automorphisms of Shift Dynamical Systems

该奖项将支持数学研究， 金教授和金教授在遍历理论的一个分支中， 象征动力学 符号动力系统是一个集合 有限字母表中的双向无限符号串 满足指定哪些符号 当一个人沿着绳子移动时， 两个这样 系统是等价的，如果有一个行为良好的双射 在它们之间，尊重换档操作。 中央 这一领域的主题是符号动力学的分类 系统的各种形式的等价物。象征性 动力系统最近已广泛应用于 数据传输的建模。 主要研究人员将研究强转移 正整数上的等价，有理数上的等价， 环上的强sofic移位等价 理性他们还将考虑移位的自同构 动力系统，特别是周期点，枚举 自同构和自同构群的子群。

This award will support the mathematical research of Professors Kim and Roush 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 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 with respect to various forms of equivalence. Symbolic dynamical systems have recently found widespread application in the modeling of data transmission. The principal investigators will study strong shift equivalence over the positive integers, over the rationals, and over general rings, and strong sofic shift equivalence over the rationals. They will also consider automorphisms of shift dynamical systems, in particular periodic points, enumeration of automorphisms, and subgroups of the automorphism group.