Singularity Analysis of 2D Complexified Hamiltonian Systems
The connection between the integrability of a differential equation and the nature of the singularities in the complex time of the solutions, has been studied by various authors since Painlevè (Bountis et. al. 1991). Recently it has been considered the connection of the integrability criterion of Painlevè and the algebraic integrability of Arnol’d-Liouville (Arnol’d 1978) for the Hamiltonian systems (M. Adler and P. van Moerbeke 1988, P. van Moerbeke 1987); unfortunately the family of algebraic integrable systems is very poor with respect to integrable systems according to Arnol’d-Liouville. On the other hand some non-integrability criteria have been established for the Hamiltonian systems (V.V. Kozlov 1983).
KeywordsRiemann Surface Hamiltonian System Analytic Continuation Action Variable Angle Variable
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