  An important problem in the dynamics of surface homeomorphisms is determining
the forcing relation between orbits. The forcing relation between periodic
orbits can be computed using standard algorithms, though this does not give
much information on the structure of the forcing relation. Here we consider
forcing relations between homoclinic orbits, and their relationships with
periodic orbits. We outline a general procedure for computing the forcing
relation, and apply this to compute the equivalence and forcing relations for
homoclinic orbits of the Smale horseshoe map. We also outline a method for
determining forcing relations from graph maps, which allows us to compute the
forcing relation between the so-called star homoclinic orbits.
