A generalization of Nekhoroshev’s theorem
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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 . 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  and is similar to what Nekhoroshev’s theorem does in the abelian case.
Keywordsperiodic orbits Hamiltonian systems
MSC2010 numbers53D50 81S10
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