Topological Speedups For Minimal Cantor Systems

TL;DR

This paper characterizes when one minimal Cantor system can be obtained as a speedup of another, extending measure-theoretic results to the topological setting and analyzing strong speedups with limited discontinuities.

Contribution

It provides topological characterizations of speedups and strong speedups for minimal Cantor systems, linking to orbit equivalence and measure-theoretic frameworks.

Findings

Characterization of when one minimal homeomorphism is a speedup of another.

Topological criteria for strong speedups with at most one discontinuity.

Connections established between topological speedups and orbit equivalence.

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.