  We describe a rigorous and efficient computer algorithm for building a model
of the dynamics of a polynomial diffeomorphism of C^2 on its chain recurrent
set, and for sorting points into approximate chain transitive components.
Further, we give explicit estimates which quantify how well this algorithm
approximates the chain recurrent set and distinguishes the chain transitive
components. We also discuss our implementation for the family of Henon
mappings, f_{a,c}(x,y) = (x^2 + c - ay, x), into a computer program called
Hypatia, and give several examples of running Hypatia on Henon mappings.
