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.
