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A Generalization of Nekhoroshev’s Theorem
Larry Bates, Richard Cushman Department of Mathematics and Statistics, University of Calgary,
Calgary, Alberta, T2N 1N4, Canada
Abstract:
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.
Keywords:
periodic orbits, Hamiltonian systems.
Received: 08.03.2016 Accepted: 05.10.2016
Citation:
Larry Bates, Richard Cushman, “A Generalization of Nekhoroshev’s Theorem”, Regul. Chaotic Dyn., 21:6 (2016), 639–642
Linking options:
https://www.mathnet.ru/eng/rcd214 https://www.mathnet.ru/eng/rcd/v21/i6/p639
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Abstract page: | 210 | References: | 26 |
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