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Zbl 1108.65121
Csendes, Tibor; Bánhelyi, Balázs; Hatvani, László
Towards a computer-assisted proof for chaos in a forced damped pendulum equation. (English)
[J] J. Comput. Appl. Math. 199, No. 2, 378-383 (2007). ISSN 0377-0427

Summary: We report on the first steps made towards the computational proof of the chaotic behaviour of the forced damped pendulum. Although, chaos for this pendulum was being conjectured for long, and it has been plausible on the basis of numerical simulations, there is no rigorous proof for it. In the present paper we provide computational details on a fitting model and on a verified method of solution. We also give guaranteed reliability solutions showing some trajectory properties necessary for complicate chaotic behaviour.

MSC 2000:: *65P20 Numerical chaos
65G40 General methods in interval analysis
37D45 Strange attractors, chaotic dynamics

Keywords: differential equations; chaos; pendulum; interval method; numerical examples; fitting model; verified method; guaranteed reliability solutions

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