Titlebook: KdV & KAM; Thomas Kappeler,Jürgen P?schel Book 2003 Springer-Verlag Berlin Heidelberg 2003 Calculation.Finite.Integrable Systems.KAM Theor

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Thomas Kappeler,Jürgen P?schelc programs to the higher-order setting of the simply typed .-calculus, where programs are presented by conditional pattern rewrite systems. Our approach generalizes and combines declarative debugging techniques previously developed for less expressive declarative programming paradigms involving appl

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Classical Background,In this book we consider the periodic KdV equation as an . integrable Hamiltonian system, and subject it to small Hamiltonian perturbations. To this end, we extend many concepts, ideas and notions from the classical . theory, such as angle-action coordinates, Birkhoff normal forms, and in particular KAM theory.

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Birkhoff Coordinates,In this chapter we consider the KdV equation . on the space .. (..) of 1-periodic functions on the real line.

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The KAM Proof,In the following we give a complete proof of the infinite dimensional KAM theorem used in chapter IV to study small Hamiltonian perturbations of KdV equations. To make this presentation independent of chapter IV we begin by recalling the set up.

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,Kuksin’s Lemma,We consider the following first order partial differential equation coming up in the proof of the classical KAM theorem: .for functions on the torus T. = ?./2.?., where ..

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Psi-Functions and Frequencies,In this appendix we prove the following theorem stated in section 8. In the form presented it is due to [6], but the proof given here is much simpler, and the normalizing constants are explicitly computed. See also [90] for prior results. — For notations we refer to sections 6 and 7.

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Birkhoff Normal Forms,Consider a Hamiltonian on the space ... introduced in section 14 of the form ., where the .. are homogeneous of degree . in . ∈ ...