Integrability in dynamical systems and the Painlevé property

  • Bernadette Dorizzi
Part of the Lecture Notes in Physics book series (LNP, volume 189)


The analytic structure of the solution of an ordinary differential equation is intimately related to its integrability. The Painlevé property, i.e., pure poles being the only movable singularities, allows the identification of new integrable dynamical systems. In this paper, we recall briefly the Ablowita-Ramani-Segur (ARS) algorithm


Ordinary Differential Equation Laurent Series Hamiltonian Integrable System Integrable Case Inverse Scattering Transform 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    [1]F. J. Bureau, Integration of some nonlinear systems of ordinary differential equations. Ann. Matematica N. 94, 344–359 (1972).Google Scholar
  2. [2]
    H. Segur, Solitons and the Inverse Scattering Transform. Lecture at the International School of Physics “Enrico Fermi” (Varenna, Italy, July 1980).Google Scholar
  3. [3]
    T. Bountis, H. Segur, and F. Vivaldi, Integrable hamiltonian systems and the Painlevé property. Phys. Rev. A25, 1257–1264 (1982).Google Scholar
  4. [4]
    M. J. Ablowitz, A. Ramani, and H. Segur, Nonlinear evolution equations and ordinary differential equations of Painlevé type. Lett. Nuovo Cimento 23, 333–338 (1978).Google Scholar
  5. [5]
    Y. F. Chang, M. Tabor, J. Weiss, and C. Corliss, On the analytic structure of the Hénon-Heiles system. Phys. Lett. 85A, 211–213 (1981).Google Scholar
  6. [6]
    J. Greene, quoted in reference 6.Google Scholar
  7. [7]
    L. J. Hall, On the existence of a last invariant of conservative motion. Annals of Physics. (Submitted.) Preprint (1982).Google Scholar
  8. [8]
    B. Grammaticos, B. Dorizzi, and R. Padjen, Painlevé property and integrals of motion for the Hénon-Heiles system. Phys. Lett. 83A, 111–113 (1982).Google Scholar
  9. [9]
    B. Grammaticos, B. Dorizzi, and A. Ramani, Integrability of hamiltonians with third and four degree polynomial potentials. J. Math. Phys. (To Appear.) Preprint (1982).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Bernadette Dorizzi
    • 1
  1. 1.Centre National d'Etude des TèlècommunicationsIssy les MoulineauxFrance

Personalised recommendations