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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.

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Correspondence to Xuezhi Zhao.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhao, X. Periodic Orbits with Least Period Three on the Circle. Fixed Point Theory Appl 2008, 194875 (2007). https://doi.org/10.1155/2008/194875

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

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