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Ukrainian Mathematical Journal

, Volume 59, Issue 1, pp 70–99 | Cite as

Invariant tori of locally Hamiltonian systems close to conditionally integrable systems

  • Yu. V. Loveikin
  • I. O. Parasyuk
Article

Abstract

We study the problem of perturbations of quasiperiodic motions in the class of locally Hamiltonian systems. By using methods of the KAM-theory, we prove a theorem on the existence of invariant tori of locally Hamiltonian systems close to conditionally integrable systems. On the basis of this theorem, we investigate the bifurcation of a Cantor set of invariant tori in the case where a Liouville-integrable system is perturbed by a locally Hamiltonian vector field and, simultaneously, the symplectic structure of the phase space is deformed.

Keywords

Hamiltonian System Poisson Bracket Poisson Structure Symplectic Structure Hamiltonian Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. V. Loveikin
    • 1
  • I. O. Parasyuk
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyiv

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