A Kam Theorem for Space-Multidimensional Hamiltonian PDE
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: 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 .
arXiv admin note: text overlap with arXiv:1502.02262