Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 194875, 8 pages
doi:10.1155/2008/194875
Research Article
Periodic Orbits with Least Period Three on the Circle
Department of Mathematics, Capital Normal University, Beijing 100037, China
Received 19 August 2007; Accepted 3 December 2007
Academic Editor: J. R. L. Webb
Copyright © 2008 Xuezhi Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The self-maps on the circle having periodic orbits with least period 3 are classified into relative homotopy-conjugacy classes. We will show that except for the maps in one exceptional class, all these kinds of maps have periodic orbits with all least periods but 2. Thus, a kind of Sharkovskii's type theorem on the circle is obtained.