Aspects of Constructive Dynamical Systems
Degree GrantorUniversity of Canterbury
Degree NameMaster of Science
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.