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Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds

Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds Let ƒ be a self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant which is the best lower bound for the number of r -periodic points for all C 1 maps homotopic to ƒ. In case m = 3 we give the formula for and calculate it for self-maps of S 2 × I . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Minimal number of periodic points for C 1 self-maps of compact simply-connected manifolds

Graff, Grzegorz; Jezierski, Jerzy
Forum Mathematicum , Volume 21 (3) – May 1, 2009
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Publisher
de Gruyter
Copyright
© de Gruyter 2009
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORUM.2009.023
Publisher site
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Abstract

Let ƒ be a self-map of a smooth compact connected and simply-connected manifold of dimension m ≥ 3, r a fixed natural number. In this paper we define a topological invariant which is the best lower bound for the number of r -periodic points for all C 1 maps homotopic to ƒ. In case m = 3 we give the formula for and calculate it for self-maps of S 2 × I .

Journal

Forum Mathematicum – de Gruyter

Published: May 1, 2009

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