Periodic points of latitudinal maps of the $m$-dimensionalsphere

Grzegorz  Graff; Michał Misiurewicz; Piotr  Nowak-Przygodzki

doi:10.3934/dcds.2016070

Article Contents

2016, Volume 36, Issue 11: 6187-6199. Doi: 10.3934/dcds.2016070

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Periodic points of latitudinal maps of the $m$-dimensional sphere

1.
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk
2.
Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202
3.
Sopot

Received: September 30, 2015

Revised: May 31, 2016

Published: May 2017

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Abstract

Let $f$ be a smooth self-map of the $m$-dimensional sphere $S^m$. Under the assumption that $f$ preserves latitudinal foliations with the fibres $S^1$, we estimate from below the number of fixed points of the iterates of $f$. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.

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Mathematics Subject Classification: Primary: 37C25, 37E30, 55M20.

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References

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