Description

• Title:
  Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
• Creator:
  Graff, Grzegorz;
  Jezierski, Jerzy;
  Myszkowski, Adrian
• Description:
  Let $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] 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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.12.10
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 2 (December 2020); 589 - 606;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.035/27403 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.035/27404
• Subject:
  Periodic points;
  smooth maps;
  Nielsen number;
  fixed point index;
  Lefschetz number;
  Primary;
  37C25;
  55M20;
  Secondary;
  37C05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.035
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other