  The complexity of a dynamical system exhibiting a homoclinic orbit is given
by the orbits that it forces. In this work we present a method, based in
pruning theory, to determine the dynamical core of a homoclinic orbit of a
Smale diffeomorphism on the 2-disk. Due to Cantwell and Conlon, this set is
uniquely determined in the isotopy class of the orbit, up a topological
conjugacy, so it contains the dynamics forced by the homoclinic orbit. Moreover
we apply the method for finding the orbits forced by certain infinite families
of homoclinic horseshoe orbits and propose its generalization to an arbitrary
Smale map.
