Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 194875, 8 pages
Research Article

Periodic Orbits with Least Period Three on the Circle

Xuezhi Zhao

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.


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.