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 be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension . We show that in the homotopy class of there is a map with less then periodic points, up to any given fixed period .

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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.