Bulletin of the
Korean Mathematical Society
BKMS

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Bull. Korean Math. Soc. 2012; 49(6): 1223-1240

Printed November 30, 2012

https://doi.org/10.4134/BKMS.2012.49.6.1223

Copyright © The Korean Mathematical Society.

A note on quasi-periodic perturbations of elliptic equilibrium points

Houyu Zhao

Chongqing Normal University

Abstract

The system $$\dot{x}=(A+\varepsilon Q(t,\varepsilon))x+\varepsilon g(t,\varepsilon)+ h(x,t,\varepsilon),$$ where $A$ is elliptic whose eigenvalues are not necessarily simple and $h$ is ${\mathcal{O}}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

Keywords: quasi-periodic perturbations, elliptic points, quasi-periodic solutions, nonresonant condition, small divisors, quasi-periodic Floquet theorem, KAM theory

MSC numbers: 37C55, 34A30, 34C20

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