TY - JOUR
AU - Rudyak, Yuli B.
AU - Schlenk, Felix
PY - 2003/03/01
Y2 - 2023/03/29
TI - Lusternik-Schnirelmann theory for fixed points of maps
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 21
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2003.011
SP - 171 - 194
AB - We use the ideas of Lusternik-Schnirelmann theory to describe the setof 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 adiscrete 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.
ER -