Mathematical Sciences: Classification and Automorphisms of Subshifts of Finite Type

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The principal investigators will study three problems in symbolic dynamics pertaining to topological classification and automorphisms of subshifts of finite type: (i) characterize strong shift equivalence for subsemirings of the nonnegative rational numbers, (ii) develop tools to understand the Williams conjecture over the nonnegative real numbers, and (iii) determine whether given permutations of the fixed points of a subshift are induced by an automorphism. This award will support research 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 with a rule of formation which specifies which symbols can follow one another. A central theme in this area is the classification of such systems with respect to various forms of equivalence. Symbolic dynamical systems have recently found application in the modelling of data transmission.