A Kam Theorem for Space-Multidimensional Hamiltonian PDE

2016/05/18 by Eliasson, L Hakan, Grebert, Benoit, Kuksin, Sergei · 1 citation
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.05457

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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