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A NOTE ON QUASI-PERIODIC PERTURBATIONS OF ELLIPTIC EQUILIBRIUM POINTS

  • Zhao, Houyu (School of Mathematics Chongqing Normal University)
  • Received : 2010.09.28
  • Published : 2012.11.30

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.

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