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The “Weak Painlevé” property and integrability of two-dimensional Hamiltonian systems

  • Basile Grammaticos
Workshop
Part of the Lecture Notes in Physics book series (LNP, volume 189)

Abstract

The integrability of dynamical systems, described by nonlinear differential equations, is associated to the singularity structure of the solutions in the complex-time plane. In this work, the usual Painlevé property, i.e., existence of poles as the only movable singularities, is somewhat extended for the case of two-dimensional hamiltonian systems. Integrability in this case is compatible with the presence of algebraic branch points of a specific nature.

Keywords

Hamiltonian System Kepler Problem Integrable Case Inverse Scattering Transform Pure Polis 
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References

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    M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, 1981.Google Scholar
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    B. Dorizzi, B. Grammaticos, and A. Ramani, A new class of integrable systems. J. Math. Phys. (To appear.)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Basile Grammaticos
    • 1
  1. 1.Centre National d'Etudes des TèlècommunicationsIssy les MoulineauxFrance

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