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arXiv · 1605.05457

A Kam Theorem for Space-Multidimensional Hamiltonian PDE

L Hakan Eliasson·Benoit Grebert·Sergei Kuksin
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Abstract

We present an abstract KAM theorem, adapted to space-multidimensional hamiltonian PDEs with smoothing non-linearities. The main novelties of this theorem are that: $\bullet$ the integrable part of the hamiltonian may contain a hyperbolic part and as a consequence the constructed invariant tori may be unstable. $\bullet$ 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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L Hakan Eliasson, Benoit Grebert, Sergei Kuksin. 2016-05-18. A Kam Theorem for Space-Multidimensional Hamiltonian PDE. https://arxiv.org/abs/1605.05457

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