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Mel’nikov-Samoilenko adiabatic stability problem

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    Ya. A. Prykarpats’kyi

  2. AGH University of Science and Technology, Krakow, Poland

    Ya. A. Prykarpats’kyi

Authors
  1. Ya. A. Prykarpats’kyi
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Additional information

Dedicated to the memory of Viktor Koz’mich Mel’nikov, colleague and teacher, a talented Moscow mathematician, without whom the theory of dynamical systems would not be so attractive.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 787–803, June, 2006.

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Prykarpats’kyi, Y.A. Mel’nikov-Samoilenko adiabatic stability problem. Ukr Math J 58, 887–903 (2006). https://doi.org/10.1007/s11253-006-0111-8

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  • DOI: https://doi.org/10.1007/s11253-006-0111-8

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