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 existing algorithms. Here we consider forcing relations between homoclinic 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.
"Forcing Relations for Homoclinic Orbits of the Smale Horseshoe Map." Experiment. Math. 14 (1) 75 - 86, 2005.