Periodic Orbits with Least Period Three on the Circle
© Xuezhi Zhao. 2008
Received: 19 August 2007
Accepted: 3 December 2007
Published: 6 December 2007
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.
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