Boundedness in Asymmetric Quasi-Periodic Oscillations

Boundedness in Asymmetric Quasi-Periodic Oscillations

Year:    2017

Author:    Xiumei Xing, Jing Ma, Lei Jiao

Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 121–128

Abstract

In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation $x′′+ax^+−bx^−+ ϕ(x) = p(t)$, where $a ≠ b$ are two positive constants and $ϕ(s)$, $p(t)$ are real analytic functions. Moreover, the $p(t)$ is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions, the quasi-periodic oscillator has the Lagrange stability. 

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2017.02.03

Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 121–128

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    boundedness quasi-periodic KAM theorem

Author Details

Xiumei Xing

Jing Ma

Lei Jiao