Computations of the least number of periodic points of smooth boundarypreserving selfmaps of simplyconnected manifolds
Abstract
Let $r$ be an odd natural number, $M$ a compact simplyconnected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simplyconnected. We consider $f$, a $C^1$ selfmaps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$periodic points for all maps preserving $\partial M$ and $C^1$homotopic to $f$. In this paper we demonstrate a purely combinatorial method of calculation of the invariant and illustrate it in various cases.
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 Category:
 Articles
 Type:
 artykuły w czasopismach
 Published in:

Topological Methods in Nonlinear Analysis
no. 56,
pages 589  606,
ISSN: 12303429  Language:
 English
 Publication year:
 2020
 Bibliographic description:
 Graff G., Jezierski J., Myszkowski A.: Computations of the least number of periodic points of smooth boundarypreserving selfmaps of simplyconnected manifolds// Topological Methods in Nonlinear Analysis Vol. 56,iss. 2 (2020), s.589606
 DOI:
 Digital Object Identifier (open in new tab) 10.12775/tmna.2020.035
 Sources of funding:
 Verified by:
 Gdańsk University of Technology
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