Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1878–1892 | Cite as

The Poincaré-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I

  • A. M. Samoilenko
  • O. Ya. Timchishin
  • A. K. Prikarpatskii


On the basis of the geometric ideas of Poincaré and Mel'nikov, we study sufficient criteria of the transversal splitting of heteroclinic separatrix manifolds of slowly perturbed nonlinear dynamical systems with a small parameter. An example of adiabatic invariance breakdown is considered for a system on a plane.


Dynamical System Small Parameter Nonlinear Dynamical System Geometric Analysis Sufficient Criterion 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • O. Ya. Timchishin
    • 1
  • A. K. Prikarpatskii
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Institute of Applied Problems of MathematicsL'viv

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