Description

• Title:
  Lusternik-Schnirelmann theory for fixed points of maps
• Creator:
  Rudyak, Yuli B.;
  Schlenk, Felix
• Description:
  We use the ideas of Lusternik-Schnirelmann theory to describe the set of fixed points of certain homotopy equivalences of a general space. In fact, we extend Lusternik-Schnirelmann theory to pairs $(\varphi, f)$, where $\varphi$ is a homotopy equivalence of a topological space $X$ and where $f \colon X \rightarrow \mathbb R$ is a continuous function satisfying $f(\varphi(x)) < f(x)$ unless $\varphi (x) = x$; in addition, the pair $(\varphi, f)$ is supposed to satisfy a discrete analogue of the Palais-Smale condition. In order to estimate the number of fixed points of $\varphi$ in a subset of $X$, we consider different relative categories. Moreover, the theory is carried out in an equivariant setting.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2003.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 21, No 1 (March 2003); 171 - 194;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.011/9622
• Subject:
  Fixed point theory;
  Lusternik-Schnirelman theory;
  Palais-Smale condition;
  Primary 37B99;
  55M20;
  58E05;
  Secondary 55M30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2003.011
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other