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Ukrainian Mathematical Journal

, Volume 58, Issue 6, pp 887–903 | Cite as

Mel’nikov-Samoilenko adiabatic stability problem

  • Ya. A. Prykarpats’kyi
Article

Abstract

We develop a symplectic method for the investigation of invariant submanifolds of nonautonomous Hamiltonian systems and ergodic measures on them. The so-called Mel’nikov-Samoilenko problem for the case of adiabatically perturbed completely integrable oscillator-type Hamiltonian systems is studied on the basis of a new construction of “ virtual” canonical transformations.

Keywords

Hamiltonian System Hamiltonian Function Canonical Transformation Invariant Torus Integral Manifold 
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. 2006

Authors and Affiliations

  • Ya. A. Prykarpats’kyi
    • 1
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv
  2. 2.AGH University of Science and TechnologyKrakowPoland

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