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

DOI:
https://doi.org/10.1090/S0002-9939-02-06361-X

Published electronically:
February 12, 2002

MathSciNet review:
1900870

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-02-06361-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