Mathematical Sciences: RUI - Irreducible Case of Williams Conjecture

9405004 Kim在有限型子移位分类方面的进一步进展似乎依赖于解决不可约情形下的威廉姆斯猜想。该项目的重点是这一重要猜想，一旦这一主题得到解决，将试图找到关于分类的进一步结果。这种方法涉及使用回转数来给从子移位平方上的共轭到原始子移位的问题提供一种次要的障碍。这项研究属于动力系统的一般领域。一般理论在编码理论、数学语言学等领域有着广泛的应用。动力系统中的一个基本问题是确定系统何时等价于基空间的模自然变换。这项工作研究了一类称为有限型子移位的动力系统的等价问题。

9405004 Kim Further progress on classification of subshifts of finite type, one of the most important types of dynamical systems, seems to depend on resolving the Williams Conjecture in the irreducible case. The project focuses on this important conjecture and once this topic is resolved, an attempt will be made to find further results on classification. The method involves the use of gyration numbers to give a sort of secondary obstruction to the problem of going from a conjugacy on squares of subshifts to the original subshift. This research falls into the general area of dynamical systems. The general theory has many applications to areas such as coding theory and mathematical linguistics. A fundamental problem in dynamical systems is to determine when systems are equivalent modulo natural transformations of the base space. This work addresses the equivalence problem for the class of dynamical systems called subshifts of finite type.