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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Hills, Tyler Willes, "The Solenoid and Warsawanoid Are Sharkovskii Spaces" (2015). Theses and Dissertations. 6148.
Sharkovskii theorem, covering spaces, solenoid, Warsawanoid, inverse limit, Warsaw circle