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Zbl 1103.90076
Csendes, Tibor; Garay, Barnabás M.; Bánhelyi, Balázs
A verified optimization technique to locate chaotic regions of Hénon systems. (English)
[J] J. Glob. Optim. 35, No. 1, 145-160 (2006). ISSN 0925-5001; ISSN 1573-2916/e

Summary: We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.

MSC 2000:: *90C26 Nonconvex programming
37D45 Strange attractors, chaotic dynamics

Keywords: chaos; global optimization; Hénon-map; verified optimization method

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