The “Weak Painlevé” property and integrability of two-dimensional Hamiltonian systems
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.
KeywordsHamiltonian System Kepler Problem Integrable Case Inverse Scattering Transform Pure Polis
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- M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, 1981.Google Scholar
- T. Bountis and H. Segur, Logarithmic singularities and chaotic behavior in hamiltonian systems AIP Conference Proceedings, # 88, 279–292 (1982).Google Scholar
- M. Tabor and J. Weiss, Analytic structure of the Lorentz system. Phys. Rev: A24, 2157–2167 (1981); C. R. Menyuk, H. H. Chen, and Y. C. Lee, Restricted multiple three-wave interactions: Painlevé analysis, Plasma Preprint PL82-052, University of Maryland (1982).Google Scholar
- B. Dorizzi, B. Grammaticos, and A. Ramani, A new class of integrable systems. J. Math. Phys. (To appear.)Google Scholar