Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Topological Speedups, Drew Daehnhardt Ash
Topological Speedups, Drew Daehnhardt Ash
Electronic Theses and Dissertations
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, …
Follower And Extender Sets In Symbolic Dynamics, Thomas Kelly French
Follower And Extender Sets In Symbolic Dynamics, Thomas Kelly French
Electronic Theses and Dissertations
Given a word w in the language of a one-dimensional shift space X, the follower set of w, denoted FX(w), is the set of all right-infinite sequences which follow w in some point of X. Extender sets are a generalization of follower sets and are defined similarly. To a given shift space X, then, we may associate a follower set sequence {|FX(n)|} which records the number of distinct follower sets in X corresponding to words of length n. Similarly, we may define an extender set sequence {|E …