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On the growth of the number of periodic points for smooth self-maps of a compact manifold


Authors: Grzegorz Graff and Jerzy Jezierski
Journal: Proc. Amer. Math. Soc. 135 (2007), 3249-3254
MSC (2000): Primary 37C25, 55M20; Secondary 37C05
Published electronically: June 20, 2007
MathSciNet review: 2322756
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension $ m\geq 3$. We show that in the homotopy class of $ f$ there is a $ C^1$ map with less then $ r$ periodic points, up to any given fixed period $ r$.


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Additional Information

Grzegorz Graff
Affiliation: Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-952 Gdansk, Poland
Email: graff@mif.pg.gda.pl

Jerzy Jezierski
Affiliation: Institute of Applications of Mathematics, Warsaw University of Life Sciences (SGGW), Nowoursynowska 159, 00-757 Warsaw, Poland
Email: jezierski@acn.waw.pl

DOI: https://doi.org/10.1090/S0002-9939-07-08836-3
Keywords: Periodic points, $C^1$ maps, indices of iterations, Nielsen number.
Received by editor(s): March 30, 2006
Received by editor(s) in revised form: June 30, 2006
Published electronically: June 20, 2007
Additional Notes: This research was supported by KBN grant No 1 P03A 03929.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.