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.
