  In this paper we connect algebraic properties of the pair-of-pants product in
local Floer homology and Hamiltonian dynamics. We show that for an isolated
periodic orbit the product is non-uniformly nilpotent and use this fact to give
a simple proof of the Conley conjecture for closed manifolds with aspherical
symplectic form. More precisely, we prove that on a closed symplectic manifold
the mean action spectrum of a Hamiltonian diffeomorphism with isolated periodic
orbits is infinite.
