Existence of quasi-periodic solutions of the real pendulum equation

Lin Lu and Xuemei Li

Chaos, Solitons & Fractals, 2014, vol. 62-63, 23-33

Abstract: The pendulum equation x¨=-αx-δẋ-(1+f0cosω1t)sinx+f1sinω2t is considered in this paper, where f0,f1 and δ are small real parameters, the ratio of ω1 and ω2 is irrational, and frequencies ω1 and ω2 satisfy the Diophantine condition. The unperturbed system (f0=f1=δ=0) has several fixed points for different parameter α. We use KAM theory to prove that the perturbed system possesses quasi-periodic solutions in neighborhoods of those fixed points.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:62-63:y:2014:i::p:23-33

DOI: 10.1016/j.chaos.2014.03.003

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