  We study the dynamics of homogeneous isotropic FRW cosmologies with positive
spatial curvature in $f(R)$-gravity, paying special attention to the existence
of Einstein static models and only study forms of $f(R)=R^n$ for which these
static models have been shown to exist. We construct a compact state space and
identify past and future attractors of the system and recover a previously
discovered future attractor corresponding to an expanding accelerating model.
We also discuss the existence of universes which have both a past and future
bounce, a phenomenon which is absent in General Relativity.
