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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the periodic points of functions on a manifold


Author: Chung-wu Ho
Journal: Proc. Amer. Math. Soc. 130 (2002), 2625-2630
MSC (2000): Primary 37C25; Secondary 54H25, 58C30
Published electronically: February 12, 2002
MathSciNet review: 1900870
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Abstract: In a conference on fixed point theory, B. Halpern of Indiana University considered the problem of reducing the number of periodic points of a map by homotopy. He also asked whether the number of periodic points of a function could be increased by a homotopy. In this paper, we will show that for any map on a closed manifold, an arbitrarily small perturbation can always create infinitely many periodic points of arbitrarily high periods.


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Additional Information

Chung-wu Ho
Affiliation: Department of Mathematics, Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026 – and – Department of Mathematics, Evergreen Valley College, San Jose, California 95135
Email: cho@siue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06361-X
PII: S 0002-9939(02)06361-X
Keywords: Manifolds, periodic points, homotopy, digraphs
Received by editor(s): February 9, 1999
Received by editor(s) in revised form: April 1, 2001
Published electronically: February 12, 2002
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society