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

A. Ramani, B. Grammaticos, T. Bountis

Research output: Contribution to journalReview articlepeer-review

416 Citations (Scopus)

Abstract

We present a review of results of the so-called Painlevé 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-Painlevé" method due to Kruskal. Finally a section is devoted to the singularity analysis of the solutions of non-integrable dynamical systems.

Original languageEnglish
Pages (from-to)159-245
Number of pages87
JournalPhysics Reports
Volume180
Issue number3
DOIs
Publication statusPublished - Aug 1989

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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