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

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

2004-05-31

arxiv.org/abs/math/0406002v2

Discrete and Continuous Dynamical Systems, Volume 15, Number 2, June 2006, pages 529--558.

Mathematics

Dynamical Systems

30 pages. 8 eps pictures. Submitted

Scientific paper

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.

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