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On the growth of the number of periodic points for smooth self-maps of a compact manifold
Author(s):
Grzegorz
Graff;
Jerzy
Jezierski
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3249-3254.
MSC (2000):
Primary 37C25, 55M20;
Secondary 37C05
Posted:
June 20, 2007
MathSciNet review:
2322756
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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  .
References:
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- [B]
- R. F. Brown, The Lefschetz Fixed Point Theorem, Glenview, New York, 1971.MR 0283793 (44:1023)
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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:
10.1090/S0002-9939-07-08836-3
PII:
S 0002-9939(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
Posted:
June 20, 2007
Additional Notes:
This research was supported by KBN grant No 1 P03A 03929.
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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