  We develop a variant of Lusternik-Schnirelmann theory for the shift operator
in equivariant Floer and symplectic homology. Our key result is that the
spectral invariants are strictly decreasing under the action of the shift
operator when periodic orbits are isolated. As an application, we prove new
multiplicity results for simple closed Reeb orbits on the standard contact
sphere, the unit cotangent bundle to the sphere and some other contact
manifolds. We also show that the lower Conley--Zehnder index enjoys a certain
recurrence property and revisit and reprove from a different perspective a
variant of the common jump theorem of Long and Zhu. This is the second,
combinatorial ingredient in the proof of the multiplicity results.
