Journal of Global Optimization

, Volume 35, Issue 1, pp 145–160 | Cite as

A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

  • Tibor Csendes
  • Barnabás M. Garay
  • Balázs Bánhelyi


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.


chaos global optimization Hénon-map verified optimization method 


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Copyright information

© Springer 2006

Authors and Affiliations

  • Tibor Csendes
    • 1
  • Barnabás M. Garay
    • 2
  • Balázs Bánhelyi
    • 1
  1. 1.Institute of InformaticsUniversity of SzegedSzegedHungary
  2. 2.Institute of MathematicsBudapest University of TechnologyBudapestHungary

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