On the periodic points of functions on a manifold
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- by Chung-wu Ho PDF
- Proc. Amer. Math. Soc. 130 (2002), 2625-2630 Request permission
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.References
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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
- ORCID: 0000-0002-6889-259X
- Email: cho@siue.edu
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1900870