A Sharkovsky theorem for non-locally connected spaces

G. Conner; Christopher P. Grant; Mark H. Meilstrup

doi:10.3934/dcds.2012.32.3485

Article Contents

2012, Volume 32, Issue 10: 3485-3499. Doi: 10.3934/dcds.2012.32.3485

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A Sharkovsky theorem for non-locally connected spaces

1.
Department of Mathematics, Brigham Young University, Provo, UT 84602
2.
Mathematics Department, Southern Utah University, Cedar City, UT, 84720

Received: March 31, 2011

Revised: July 31, 2011

Published: September 2012

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Abstract

We extend Sharkovsky's Theorem to several new classes of spaces, which include some well-known examples of non-locally connected continua, such as the topologist's sine curve and the Warsaw circle. In some of these examples the theorem applies directly (with the same ordering), and in other examples the theorem requires an altered partial ordering on the integers. In the latter case, we describe all possible sets of periods for functions on such spaces, which are based on multiples of Sharkovsky's order.

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Mathematics Subject Classification: Primary: 37E15.

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