Bratteli diagrams for bounded topological speedups

Abstract

ABSTRACT A bounded topological speedup of a Cantor minimal system is a minimal system , where for some bounded function , or any system topologically conjugate to such an . Assuming the system is represented by a properly ordered Bratteli diagram , we provide a method for constructing a new, perfectly ordered Bratteli diagram that represents the sped-up system . The diagram relates back to in a manner that enables us to see how certain dynamical properties are preserved under speedup. As an application, in the case that is a substitution minimal system, we show how to use to write an explicit substitution rule that generates the sped-up system , answering an open question from [L. Alvin, D.D. Ash, and N.S. Ormes, Bounded topological speedups, Dyn. Syst. 33(2) (2018), pp. 303–331.].