A note on quasi-periodic perturbations of elliptic equilibrium points
Bull. Korean Math. Soc. 2012 Vol. 49, No. 6, 1223-1240
https://doi.org/10.4134/BKMS.2012.49.6.1223
Published online November 30, 2012
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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