Geodesic
A KAM theorem for space-multidimensional Hamiltonian PDEs
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 142-162

Voir la notice de l'article provenant de la source Math-Net.Ru

We present an abstract KAM theorem adapted to space-multidimensional Hamiltonian PDEs with smoothing nonlinearities. The main novelties of this theorem are the following: (i) the integrable part of the Hamiltonian may contain a hyperbolic part and, as a consequence, the constructed invariant tori may be unstable; (ii) it applies to singular perturbation problems. 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. 
@article{TM_2016_295_a6,
     author = {L. H. Eliasson and B. Gr\'ebert and S. B. Kuksin},
     title = {A {KAM} theorem for space-multidimensional {Hamiltonian} {PDEs}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {142--162},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_295_a6/}
}
TY  - JOUR
AU  - L. H. Eliasson
AU  - B. Grébert
AU  - S. B. Kuksin
TI  - A KAM theorem for space-multidimensional Hamiltonian PDEs
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2016
SP  - 142
EP  - 162
VL  - 295
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2016_295_a6/
LA  - ru
ID  - TM_2016_295_a6
ER  - 
%0 Journal Article
%A L. H. Eliasson
%A B. Grébert
%A S. B. Kuksin
%T A KAM theorem for space-multidimensional Hamiltonian PDEs
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2016
%P 142-162
%V 295
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2016_295_a6/
%G ru
%F TM_2016_295_a6
L. H. Eliasson; B. Grébert; S. B. Kuksin. A KAM theorem for space-multidimensional Hamiltonian PDEs. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 142-162. http://geodesic.mathdoc.fr/item/TM_2016_295_a6/