American Institute of Mathematical Sciences

November  2016, 36(11): 6187-6199. doi: 10.3934/dcds.2016070

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, Poland 2 Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202 3 Sopot, Poland

Received  October 2015 Revised  June 2016 Published  August 2016

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.
Citation: Grzegorz Graff, Michał Misiurewicz, Piotr Nowak-Przygodzki. Periodic points of latitudinal maps of the $m$-dimensional sphere. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6187-6199. doi: 10.3934/dcds.2016070
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