Regular and Chaotic Dynamics

, Volume 21, Issue 6, pp 639–642 | Cite as

A generalization of Nekhoroshev’s theorem

  • Larry Bates
  • Richard Cushman
On the 70th Birthday of Nikolai N. Nekhoroshev Special Memorial Issue. Part 1


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.


periodic orbits Hamiltonian systems 

MSC2010 numbers

53D50 81S10 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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