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

Balázs Lévai () and Balázs Bánhelyi ()

Central European Journal of Operations Research, 2013, vol. 21, issue 4, 757-767

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

Keywords: Forced damped pendulum; Rigorous methods; Optimization technique; Chaotic behaviour (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10100-012-0256-5

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