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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.