Abstract
We extend Sharkovskii's theorem concerning orbit lengths of endomorphisms of the real line to endomorphisms of a path component of the solenoid and certain subspaces of the Warsawanoid. In particular, Sharkovskii showed that if there exists an orbit of length 3 then there exist orbits of all lengths. The solenoid is the inverse limit of double covers over the circle, and the Warsawanoid is the inverse limit of double covers over the Warsaw circle. We show Sharkovskii's result is true for path components of the solenoid and certain subspaces of the Warsawanoid.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Hills, Tyler Willes, "The Solenoid and Warsawanoid Are Sharkovskii Spaces" (2015). Theses and Dissertations. 6148.
https://scholarsarchive.byu.edu/etd/6148
Date Submitted
2015-12-01
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd8303
Keywords
Sharkovskii theorem, covering spaces, solenoid, Warsawanoid, inverse limit, Warsaw circle
Language
english