@article{Rudyak_Schlenk_2003, title={Lusternik-Schnirelmann theory for fixed points of maps}, volume={21}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2003.011}, abstractNote={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.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Rudyak, Yuli B. and Schlenk, Felix}, year={2003}, month={Mar.}, pages={171–194} }