The almost-periodic solutions of the weakly coupled pendulum equations

Advances in Difference Equations

卷:2018

Hepeng Li¹ 

[1] School of Mathematical Sciences, Fudan University;

关键词: Coupled pendulum equations;    Normally hyperbolic invariant tori;    Almost-periodic solutions;    KAM theory;   

DOI  :  10.1186/s13662-018-1604-0

来源: DOAJ

【 摘 要 】

Abstract In this paper, it is proved that, for the networks of weakly coupled pendulum equations d2xndt2+λn2sinxn=ϵWn(xn−1,xn,xn−1),n∈Z, $$\frac{d^{2} x_{n}}{d t^{2}}+\lambda_{n}^{2} \sin x_{n}= \epsilon W_{n}(x_{n-1},x_{n},x_{n-1}),\quad n \in\mathbb {Z}, $$ there are many (positive Lebesgue measure) normally hyperbolic invariant tori which are infinite dimensional in both tangent and normal directions.

【 授权许可】

Unknown