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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2016, том 21, выпуск 6, страницы 639–642 (Mi rcd214)

A Generalization of Nekhoroshev’s Theorem

Larry Bates, Richard Cushman

Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

Аннотация: Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville–Arnol’d on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev’s theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev’s theorem does in the abelian case.

Ключевые слова: periodic orbits, Hamiltonian systems.

MSC: 53D50, 81S10

Поступила в редакцию: 08.03.2016
Принята в печать: 05.10.2016

Язык публикации: английский

DOI: 10.1134/S1560354716060046



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