Aspects of Constructive Dynamical Systems

Type of content
Theses / Dissertations
Publisher's DOI/URI
Thesis discipline
Mathematics
Degree name
Master of Science
Publisher
University of Canterbury. Mathematics and Statistics
Journal Title
Journal ISSN
Volume Title
Language
Date
2009
Authors
Hendtlass, Matthew Ralph John
Abstract

We give a Bishop-style constructive analysis of the statement that a continuous homomorphism from the real line onto a compact metric abelian group is periodic; constructive versions of this statement and its contrapositive are given. It is shown that the existence of a minimal period in general is not derivable, but the minimal period is derivable under a simple geometric condition when the group is contained in two dimensional Euclidean space. A number of results about one-one and injective mappings are proved en route to our main theorems. A few Brouwerian examples show that some of our results are the best possible in a constructive framework.

Description
Citation
Keywords
Constructive mathematics, compact group, periodic
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Rights
Copyright Matthew Ralph John Hendtlass