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arXiv · 1102.1066

Quasi-T\"oplitz functions in KAM theorem

Xindong Xu·Michela Procesi
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Abstract

We define and describe the class of Quasi-T\"oplitz functions. We then prove an abstract KAM theorem where the perturbation is in this class. We apply this theorem to a Non-Linear-Scr\"odinger equation on the torus $T^d$, thus proving existence and stability of quasi-periodic solutions and recovering the results of [10]. With respect to that paper we consider only the NLS which preserves the total Momentum and exploit this conserved quantity in order to simplify our treatment.

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Xindong Xu, Michela Procesi. 2011-02-05. Quasi-T\"oplitz functions in KAM theorem. https://doi.org/10.1137/110833014

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