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

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 th...

Full description

Saved in:
Bibliographic Details
Main Authors: Lévai Balázs László
Bánhelyi Balázs
Format: Article
Published: Springer 2013
Series:CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 21 No. 4
doi:10.1007/s10100-012-0256-5

mtmt:2194515
Online Access:http://publicatio.bibl.u-szeged.hu/9122
Description
Summary: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 trajectorieswith arbitrary precision, the present paper establishes an optimization method capable to locate finite trajectory segments with prescribed geometrical behavior.
Physical Description:757-767
ISSN:1435-246X