  We extend Lusternik-Schnirelmann theory to pairs $(f, \phi)$, where $\phi$ is
a homotopy equivalence of a space $X$, $f$ is a function on $X$ which decreases
along $\phi$ and $(f, \phi)$ satisfies a discrete analog of the Palais-Smale
condition. The theory is carried out in an equivariant setting.
