Open Access

Periodic Orbits with Least Period Three on the Circle

Fixed Point Theory and Applications20072008:194875

https://doi.org/10.1155/2008/194875

Received: 19 August 2007

Accepted: 3 December 2007

Published: 6 December 2007

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Capital Normal University

Copyright

© Xuezhi Zhao. 2008

This article is published under license to BioMed Central Ltd. 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.