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2003 Lusternik-Schnirelmann theory for fixed points of maps
Yuli B. Rudyak, Felix Schlenk
Topol. Methods Nonlinear Anal. 21(1): 171-194 (2003).


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.


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Yuli B. Rudyak. Felix Schlenk. "Lusternik-Schnirelmann theory for fixed points of maps." Topol. Methods Nonlinear Anal. 21 (1) 171 - 194, 2003.


Published: 2003
First available in Project Euclid: 30 September 2016

zbMATH: 1044.37011
MathSciNet: MR1980143

Rights: Copyright © 2003 Juliusz P. Schauder Centre for Nonlinear Studies


Vol.21 • No. 1 • 2003
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