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

Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets