UBC Ergodic Theory Seminar: Sophie MacDonald

A number of results in symbolic dynamics, principally Krieger’s embedding theorem and Boyle’s lower-entropy factor theorem, give conditions for the existence of an injective or surjecive sliding block code from one subshift to another, in terms of entropy and low-order periodic points. I will present a recent result answering the following question of Tom Meyerovitch: given a surjective sliding block code from a mixing shift of finite type X to a mixing sofic shift Y, for which subshifts Z of strictly lower entropy than Y does there exist a sliding block code from Z into X such that the composition (from Z into Y) is injective? The result can be seen as a deterministic analogue of various results in information theory, giving conditions, in terms of entropy and periodic points, on the sources which can be transmitted without error through a deterministic channel (i.e. a sliding block code) despite deterministic noise (i.e. non-injectivity).