#### Degree Type

Dissertation

#### Date of Award

1987

#### Degree Name

Doctor of Philosophy

#### Department

Mathematics

#### First Advisor

Justin Peters

#### Abstract

Let X be compact Hausdorff, [sigma] the natural numbers or integers, [phi]: X → X, and [phi][superscript] k: k ϵ [sigma] a (semi)group of continuous functions from X to X. Given the dynamical system (X,[phi],[sigma]), let U be a [sigma]-invariant C[superscript]*-algebra of bounded functions containing C(X). There is a natural extension (X,[phi],[sigma]) of (X,[phi],[sigma]) where X is the spectrum of U and [phi] is given by [phi](x)f = x(f ∘ [phi]). If U has a dense subset of functions continuous on a cofinite set, then (X, [phi],[sigma]) inherits the properties of minimality and topological transitivity from (X,[phi],[sigma]) if and only if U contains no point characteristic functions;If X is the circle, [phi] an irrational rotation, and U the C[superscript]*-algebra generated by C(X) and [xi] ∘ [phi][superscript] k, k ϵ Z, where the bounded function [xi] is continuous on X 0, then (X,[phi],Z) preserves the zero topological entropy of (X,[phi],Z) but does not inherit the distality of (X,[phi],Z). (X,[phi],Z) may or may not be expansive depending on the function [xi].

#### DOI

https://doi.org/10.31274/rtd-180813-13110

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

#### Copyright Owner

Timothy James Pennings

#### Copyright Date

1987

#### Language

en

#### Proquest ID

AAI8805124

#### File Format

application/pdf

#### File Size

45 pages

#### Recommended Citation

Pennings, Timothy James, "Extensions of dynamical systems " (1987). *Retrospective Theses and Dissertations*. 9289.

https://lib.dr.iastate.edu/rtd/9289