On the periodic points of functions on a manifold
Author:
Chungwu Ho
Journal:
Proc. Amer. Math. Soc. 130 (2002), 26252630
MSC (2000):
Primary 37C25; Secondary 54H25, 58C30
Published electronically:
February 12, 2002
MathSciNet review:
1900870
Fulltext PDF Free Access
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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
Chungwu 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/S000299390206361X
PII:
S 00029939(02)06361X
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
