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An abstract KAM theorem

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 Added by Mauricio D. Garay
 Publication date 2013
  fields
and research's language is English




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The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.



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96 - Shidi Zhou 2017
In this paper we consider nonlinear Schrodinger systems with periodic boundary condition in high dimension. We establish an abstract infinite dimensional KAM theorem and apply it to the nonlinear Schrodinger equation systems with real Fourier Multiplier. By establishing a block-diagonal normal form, We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.
200 - Joachim Albrecht 2007
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the theorem presented here is to provide exactly the estimates needed in [1].
In this paper we consider the completely resonant beam equation on T^2 with cubic nonlinearity on a subspace of L^2 (T^2) which will be explained later. We establish an abstract infinite dimensional KAM theorem and apply it to the completely resonant beam equation. We prove the existence of a class of Whitney smooth small amplitude quasi-periodic solutions corresponding to finite dimensional tori.
82 - Abed Bounemoura 2020
We propose a slight correction and a slight improvement on the main result contained in A lecture on Classical KAM Theorem by J. P{o}schel.
120 - Mauricio Garay 2015
Lectures given on KAM theory at the University of Ouargla (Algeria). I present a functional analytic treatment of the subject which includes KAM theory into the general framework of deformations and singularity theory.
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