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.
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This research was partially supported by the TAMOP-4.2.2/08/1/2008-0008 program of the Hungarian National Development Agency, by the European Union and co-financed by the European Regional Development Fund within the project TAMOP-4.2.1/B-09/1/KONV-2010-0005, and by the Japanese-Hungarian bilaterial project JP-28/09.
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Lévai, B.L., Bánhelyi, B. An optimization technique for verified location of trajectories with prescribed geometrical behaviour in the chaotic forced damped pendulum. Cent Eur J Oper Res 21, 757–767 (2013). https://doi.org/10.1007/s10100-012-0256-5
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DOI: https://doi.org/10.1007/s10100-012-0256-5