Date of Award

1-1-2016

Document Type

Dissertation

Degree Name

Ph.D.

First Advisor

Nicholas S. Ormes, Ph.D.

Second Advisor

Ronnie Pavlov

Third Advisor

Frederic Latremoliere

Fourth Advisor

Susan Sadler

Keywords

Ergodic theory, Orbit equivalence, Speedups, Topological dynamics

Abstract

Given a dynamical system T:X rightarrow X one can define a speedup of (X,T) as another dynamical system conjugate to S:X rightarrow X where S(x)=T^{p(x)}(x) for some function p:X rightarrowZ^{+}. In 1985 Arnoux, Ornstein, and Weiss showed that any aperiodic measure preserving system is isomorphic to a speedup of any ergodic measure preserving system. In this thesis we study speedups in the topological category. Specifically, we consider minimal homeomorphisms on Cantor spaces. Our main theorem gives conditions on when one such system is a speedup of another. Moreover, the main theorem serves as a topological analogue of the Arnoux, Ornstein, and Weiss speedup theorem, as well as a one-sided analogue of Giordano, Putnam, and Skau's characterization of orbit equivalence. Further, this thesis explores the special case of speedups when the p function is bounded. In this case, we provide bounds on the entropy of bounded speedups.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Drew Daehnhardt Ash

Provenance

Received from ProQuest

File Format

application/pdf

Language

en

File Size

99 p.

Discipline

Mathematics

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Mathematics Commons

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