Commentarii Mathematici Helvetici

, Volume 64, Issue 1, pp 84–132

KAM theory in configuration space


  • Dietmar Salamon
    • Mathematics InstituteUniversity of Warwick
    • ETH-Zeutrum
  • Eduard Zehnder
    • Mathematics InstituteUniversity of Warwick
    • ETH-Zeutrum

DOI: 10.1007/BF02564665

Cite this article as:
Salamon, D. & Zehnder, E. Commentarii Mathematici Helvetici (1989) 64: 84. doi:10.1007/BF02564665


A new approach to the Kolmogorov-Arnold-Moser theory concerning the existence of invariant tori having prescribed frequencies is presented. It is based on the Lagrangian formalism in configuration space instead of the Hamiltonian formalism in phase space used in earlier approaches. In particular, the construction of the invariant tori avoids the composition of infinitely many coordinate transformations. The regularity results obtained are applied to invariant curves of monotone twist maps. The Lagrangian approach has been prompted by a recent study of minimal foliations for variational problems on a torus by J. Moser.

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© Birkhäuser Verlag 1989