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May  2006, 15(2): 529-558. doi: 10.3934/dcds.2006.15.529

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

Suzanne Lynch Hruska 1,

1. 

Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405, United States

Received  January 2005 Revised  October 2005 Published  March 2006

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.
Keywords: pseudotrajectories, recurrence, rigorous numerics, Hénon maps, complex dynamics..
Mathematics Subject Classification: 32H50, 37C50, 37B35, 37-04, 37F10, 37F5.
Citation: Suzanne Lynch Hruska. Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 529-558. doi: 10.3934/dcds.2006.15.529
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