Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems
type: Item
instance of: scholarly article
title: Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems
zbMATH Open document ID: 0631.70012
DOI: 10.1007/BF00046688
author: Haruo Yoshida
author: B. Grammaticos
author: A. Ramani
published in: Acta Applicandae Mathematicae
publication date: 1987-01-01T00:00:00Z
review text: The paper presents a detailed review of the relation between integrability of a system and the analytic properties of the solution of the equations of motion in the complex time plane. Three different approaches are considered: Yoshida's method [e.g.: \textit{H. Yoshida}, Celestial Mech. 31, 381-399 (1983; Zbl 0556.70015)], the ``weak Painlevé'' approach and Ziglin's method [e.g.: \textit{S. L. Ziglin}, Funkts. Anal. Prilozh. 17, No.1, 8-23 (1983; Zbl 0518.58016)]. Among others, the authors derive an extension of Ziglin's theorem on nonintegrability.
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 4026877
zbMATH Keywords: singularity analysis
zbMATH Keywords: integrability of a system
zbMATH Keywords: analytic properties of the solution
zbMATH Keywords: equations of motion
zbMATH Keywords: complex time plane
zbMATH Keywords: Yoshida's method
zbMATH Keywords: ``weak Painlevé'' approach
zbMATH Keywords: Ziglin's method
zbMATH Keywords: theorem on nonintegrability
reviewed by: József Szilasi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00046688
OpenAlex ID: W1978926443
description: scientific article; zbMATH DE number 4026877