Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 194875, 8 pages
doi:10.1155/2008/194875

Periodic orbits with least period three on the circle

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.