On quasi-periodic perturbations of hyperbolic-type degenerateequilibrium point of a class of planar systems

Junxiang Xu

doi:10.3934/dcds.2013.33.2593

Article Contents

2013, Volume 33, Issue 6: 2593-2619. Doi: 10.3934/dcds.2013.33.2593

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On quasi-periodic perturbations of hyperbolic-type degenerate equilibrium point of a class of planar systems

Junxiang Xu^1,

1.
Department of Mathematics, Southeast University, Nanjing 210096

Received: October 31, 2011

Revised: September 30, 2012

Published: June 2013

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Abstract

In this paper we consider two-dimensional nonlinear quasi-periodic system with small perturbations. Assume that the unperturbed system has a hyperbolic-type degenerate equilibrium point and the frequency satisfies the Diophantine conditions. Using the KAM iteration we prove that for sufficiently small perturbations, the system can be reduced by a nonlinear quasi-periodic transformation to a suitable normal form with an equilibrium point at the origin. Hence, for the system we can obtain a small quasi-periodic solution.

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Mathematics Subject Classification: Primary: 34J40, 34C27; Secondary: 34E20.

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