Description

• Title:
  Wecken property for periodic points on the Klein bottle
• Creator:
  Jezierski, Jerzy;
  Keppelmann, Edward;
  Marzantowicz, Wacław
• Description:
  Suppose $f\colon M\to M$ on a compact manifold. Let $m$ be a natural number. One of the most important questions in the topological theory of periodic points is whether the Nielsen-Jiang periodic number $NF_m(f)$ is a sharp lower bound on $\# \text{\rm Fix}(g^m)$ over all $g\sim f$. This question has a positive answer if $\text{\rm dim} M\geq 3$ but in general a negative answer for self maps of compact surfaces. However, we show the answer to be positive when $M={\mathbb K}$ is the Klein bottle. As a consequence, we reconfirm a result of Llibre and compute the set $\text{\rm HPer} (f)$ of homotopy minimal periods on the Klein bottle.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 1 (March 2009); 51 - 64;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.005/8602
• Subject:
  Periodic point;
  homotopy minimal period;
  Nielsen number;
  Nielsen-Jiang periodic number;
  Klein bottle;
  55M20;
  57N99
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.005
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other