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/

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

Included in

Mathematics Commons

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