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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 142–162
DOI: https://doi.org/10.1134/S0371968516040075 (Mi tm3751) 		 
This article is cited in 1 scientific paper (total in 1 paper)

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
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DOI: https://doi.org/10.1134/S0371968516040075
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.
Received: June 14, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 129–147
DOI: https://doi.org/10.1134/S0081543816080071
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: L. H. Eliasson, B. Grébert, S. B. Kuksin, “A KAM theorem for space-multidimensional Hamiltonian PDEs”, Modern problems of mechanics, Collected papers, Trudy 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
\serial Trudy Mat. Inst. Steklova
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\vol 295
\pages 142--162
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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