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On the periodic points of functions on a manifold
Author(s):
Chung-wu
Ho
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2625-2630.
MSC (2000):
Primary 37C25;
Secondary 54H25, 58C30
Posted:
February 12, 2002
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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:
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
Posted:
February 12, 2002
Communicated by:
Alan Dow
Copyright of article:
Copyright
2002,
American Mathematical Society
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