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

We describe a rigorous and efficient computer algorithm for building a model of the dynamics of a polynomial diffeomorphism of C² on its chain recurrent set, $R$, 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 Hénon 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 Hénon mappings.