Topological Speedups For Minimal Cantor Systems

Abstract

In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong speedups, i.e., when the jump function has at most one point of discontinuity. These results provide topological versions of the measure-theoretic results of Arnoux, Ornstein and Weiss, and are closely related to Giordano, Putnam and Skau's characterization of orbit equivalence for minimal Cantor systems.

32 pages, to appear in Israel Journal of Mathematics. Corrected and expanded version of "Topological Speedups'' by Ash