Integrable Hamiltonian systems and the Painlevé property

Tassos Bountis, Harvey Segur, Franco Vivaldi

Research output: Contribution to journalArticlepeer-review

179 Citations (Scopus)


A direct method is described for obtaining conditions under which certain N-degree-of-freedom Hamiltonian systems are integrable, i.e., possess N integrals in involution. This method consists of requiring that the general solutions have the Painlevé property, i.e., no movable singularities other than poles. We apply this method to several Hamiltonian systems of physical significance such as the generalized Hénon-Heiles problem and the Toda lattice with N=2 and 3, and recover all known integrable cases together with a few new ones. For some of these cases the second integral is written down explicitly while for others integrability is confirmed by numerical experiments.

Original languageEnglish
Pages (from-to)1257-1264
Number of pages8
JournalPhysical Review A
Issue number3
Publication statusPublished - Jan 1 1982

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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