Integrable Hamiltonian Systems and Poisson Actions with Simple Singular Points

  • Lev M. Lerman
  • Yan L. Umanskii
Part of the NATO ASI Series book series (NSSB, volume 331)


The integrable Hamiltonian systems possessing singular points play a specific role in applications to the nonlinear equations of mathematical physics. Especially it concerns separatrix sets of singular points because they relate with a description of soliton solutions of such equations. On the other hand these sets are used in various perturbation methods like the Mel’nikov method for detecting nonintegrability and chaos.


Vector Field Singular Point Unstable Manifold Stable Manifold Integrable Hamiltonian System 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Lev M. Lerman
    • 1
  • Yan L. Umanskii
    • 2
  1. 1.Research Institute for Applied Mathematics & CyberneticsNizhny NovgorodRussia
  2. 2.Department of MathematicsAgricultural InstituteNizhny NovgorodRussia

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