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An optimization technique for verified location of trajectories with prescribed geometrical behaviour in the chaotic forced damped pendulum

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  • Balázs Lévai
  • Balázs Bánhelyi

Abstract

The present paper studies the forced damped pendulum equation, equipped with Hubbard’s parameters (Hubbard in Am Math Mon 8:741–758, 1999 ). With the aid of rigorous computations, his 1999 conjecture on the existence of chaos was proved in Bánhelyi et al. (SIAM J Appl Dyn Syst 7:843–867, 2008 ) but the problem of finding chaotic trajectories remained entirely open. In order to approximate a wide range of chaotic trajectories with arbitrary precision, the present paper establishes an optimization method capable to locate finite trajectory segments with prescribed geometrical behavior. Copyright Springer-Verlag 2013

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  • Balázs Lévai & Balázs Bánhelyi, 2013. "An optimization technique for verified location of trajectories with prescribed geometrical behaviour in the chaotic forced damped pendulum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 757-767, December.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:4:p:757-767
    DOI: 10.1007/s10100-012-0256-5
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    References listed on IDEAS

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    1. Maziar Salahi, 2010. "Convex optimization approach to a single quadratically constrained quadratic minimization problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 181-187, June.
    2. Balázs Torma & Boglárka G.-Tóth, 2010. "An efficient descent direction method with cutting planes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 105-130, June.
    3. Mateusz Tykierko, 2007. "Using invariants to determine change detection in dynamical system with chaos," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(3), pages 223-233, September.
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