Abstract
In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim of this paper is twofold. One is to establish the linear stability of the perturbed invariant tori by using the CWB method without the second Melnikov condition. The other one is to illustrate the CWB method in detail and make the CWB method more accessible.
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