Ukrainian Mathematical Journal

, Volume 51, Issue 11, pp 1713–1728 | Cite as

Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable Hamiltonian systems. II

  • A. M. Samoilenko
  • Ya A. Prikarpatskii


By using the Cartan differential-geometric theory of integral submanifolds (invariant tori) of completely Liouville—Arnold integrable Hamiltonian systems on the cotangent phase space, we consider an algebraic-analytical method for the investigation of the corresponding mapping of imbedding of an invariant torus into the phase space. This enables one to describe analytically the structure of quasiperiodic solutions of the Hamiltonian system under consideration. We also consider the problem of existence of adiabatic invariants associated with a slowly perturbed Hamiltonian system.


Riemannian Surface Hamiltonian System Symplectic Structure Hamiltonian Function Canonical Transformation 
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Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • Ya A. Prikarpatskii
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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