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Pré-Publication, Document De Travail Année : 2016

A KAM THEOREM FOR SPACE-MULTIDIMENSIONAL HAMILTONIAN PDE

Résumé

We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: • the integrable part of the hamiltonian may contain a hyperbolic part and as a consequence the constructed invariant tori may be unstable. • It applies to singular perturbation problem. In this paper we state the KAM-theorem and comment on it, give the main ingredients of the proof, and present three applications of the theorem .
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Dates et versions

hal-01316395 , version 1 (17-05-2016)
hal-01316395 , version 2 (10-06-2016)

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L Hakan Eliasson, Benoit Grebert, Sergei Kuksin. A KAM THEOREM FOR SPACE-MULTIDIMENSIONAL HAMILTONIAN PDE. 2016. ⟨hal-01316395v2⟩
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