Mathematical Sciences: Stable Classification and Automorphisms of Shift Dynamical Systems

这个奖项将支持Kim教授和Roush教授在被称为符号动力学的遍历理论的一个分支中进行的数学研究。符号动力系统是来自有限字母表的双向无限符号串的集合，满足一个形成规则，该规则指定当一个人沿着该串移动时，允许跟随哪些符号。如果两个这样的系统之间存在遵守移位操作的行为良好的双射，则这两个系统是等价的。这一领域的一个中心主题是关于各种形式的等价性的符号动力系统的分类。近年来，符号动力系统在数据传输建模中得到了广泛的应用。主要研究人员将研究正整数、有理数和一般环上的强移位等价，以及有理数上的强SOFIC移位等价。他们还将考虑移位动力系统的自同构，特别是周期点，自同构的计数，以及自同构群的子群。

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.