Mathematical Sciences: Ergodic Theory of Symbolic Systems

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This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. The particular work to be undertaken by Professors Lind and Tuncel is in the area of "symbolic dynamics". A symbolic dynamical system is a collection of two-way infinite strings of symbols from a finite alphabet. These strings satisfy a formation rule which specifies which symbols are allowed to follow which as one moves along the string. Symbolic dynamical systems have recently found widespread application in the modelling of data transmission. Some of the particular areas of investigation will involve the dynamics of commuting automorphisms of compact groups, the construction of Markov partitions using self-similar tilings of the plane, and codings and invariants of Markov chains. The work stresses interactions between the fields of ergodic theory, algebra, and geometry.