Associate Professor of Mathematics Andrew Dykstra recently published a research article on symbolic dynamical systems in Journal d’Analyse Mathématique. Titled “The Morse Minimal System is Nearly Continuously Kakutani Equivalent to the Binary Odometer,” the article is a joint work with Ayse Sahin of Wright State University.
The article presents the results of the authors’ study of an equivalence relation called “nearly continuous Kakutani equivalence” that has generated much interest in recent years. This equivalence relation is a stronger, more topological version of the more classical Kakutani equivalence relation in the measurable category.
The main finding shows that the Morse minimal system and the binary odometer are equivalent in this stronger, more topological sense. It follows from earlier results that these two systems are then also equivalent to irrational circle rotations and other examples.