  Effects induced by the finite number $N$ of particles on the evolution of a
monochromatic electrostatic perturbation in a collisionless plasma are
investigated. For growth as well as damping of a single wave, discrete particle
numerical simulations show a $N$-dependent long time behavior which differs
from the numerical errors incurred by vlasovian approaches and follows from the
pulsating separatrix crossing dynamics of individual particles.
