The Painlevé property and singularity analysis of integrable and non-integrable systems

Abstract We present a review of results of the so-called Painleve singularity approach to the investigation of the integrability of dynamical systems with finite and infinite number of degrees of freedom. Rigorous results based on the theorems of Yoshida and Ziglin concerning proofs of non-integrability are also presented, as well as an application of the new “poly-Painleve” method due to Kruskal. Finally a section is devoted to the singularity analysis of the solutions of non-integrable dynamical systems.

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