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Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 142–162 (Mi tm3751)  

A KAM theorem for space-multidimensional Hamiltonian PDEs

L. H. Eliassona, B. Grébertb, S. B. Kuksina

a Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathéematiques de Jussieu–Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Université Paris 06, F-75013, Paris, France
b Laboratoire de Mathématiques Jean Leray, Université de Nantes, UMR CNRS 6629, 44322 Nantes Cedex 3, France

Abstract: 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.

DOI: https://doi.org/10.1134/S0371968516040075

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 129–147

Bibliographic databases:

UDC: 517.957
Received: June 14, 2016

Citation: L. H. Eliasson, B. Grébert, S. B. Kuksin, “A KAM theorem for space-multidimensional Hamiltonian PDEs”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 142–162; Proc. Steklov Inst. Math., 295 (2016), 129–147

Citation in format AMSBIB
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\paper A KAM theorem for space-multidimensional Hamiltonian PDEs
\inbook Modern problems of mechanics
\bookinfo Collected papers
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\pages 142--162
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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