English

A Kam Theorem for Space-Multidimensional Hamiltonian PDE

Analysis of PDEs 2016-06-13 v2 Dynamical Systems

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 .

Keywords

Cite

@article{arxiv.1605.05457,
  title  = {A Kam Theorem for Space-Multidimensional Hamiltonian PDE},
  author = {L Hakan Eliasson and Benoit Grebert and Sergei Kuksin},
  journal= {arXiv preprint arXiv:1605.05457},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1502.02262

R2 v1 2026-06-22T14:03:28.914Z