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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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All maps of type $2^{\infty }$ are boundary maps
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by Víctor Jiménez López and L’ubomír Snoha PDF
Proc. Amer. Math. Soc. 125 (1997), 1667-1673 Request permission

Abstract:

Let $f$ be a continuous map of an interval into itself having periodic points of period $2^{n}$ for all $n\geq 0$ and no other periods. It is shown that every neighborhood of $f$ contains a map $g$ such that the set of periods of the periodic points of $g$ is finite. This answers a question posed by L. S. Block and W. A. Coppel.
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Additional Information
  • Víctor Jiménez López
  • Affiliation: Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, Aptdo. de Correos 4021, 30100 Murcia, Spain
  • Email: vjimenez@fcu.um.es
  • L’ubomír Snoha
  • Affiliation: Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
  • MR Author ID: 250583
  • Email: snoha@bb.sanet.sk
  • Received by editor(s): February 27, 1995
  • Received by editor(s) in revised form: May 2, 1995
  • Additional Notes: Most of the work on this paper was done during the stay of the first author at the Matej Bel University. The invitation and the support of this institution is gratefully acknowledged. The first author has been partially supported by the DGICYT PB91-0575 and the second author by the Slovak grant agency, grant number 1/1470/94.
  • Communicated by: Mary Rees
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 1667-1673
  • MSC (1991): Primary 26A18; Secondary 58F08, 54H20
  • DOI: https://doi.org/10.1090/S0002-9939-97-03452-7
  • MathSciNet review: 1342034