Folding transformations of the Painlevé equations
type: Item
instance of: scholarly article
title: Folding transformations of the Painlevé equations
zbMATH Open document ID: 1073.34101
author: Teruhisa Tsuda
author: Kazuo Okamoto
author: Hidetaka Sakai
published in: Mathematische Annalen
publication date: 2005-04-15T00:00:00Z
review text: From authors' abstract: ``New symmetries of the Painlevé differential equations, called folding transformations, are determined. These transformations are not birational but algebraic transformations of degree 2, 3 or 4. These are associated with quotients of the spaces of initial conditions of each Painlevé equation. We make the complete list of such transformations up to birational symmetries. We also discuss correspondences of special solutions of Painlevé equations''. The method is based on the investigation of the Painlevé systems as Hamiltonian systems corresponding to the Painlevé equations. A folding transformation of such a system is an algebraic transformation which gives rise to a nontrivial quotient map of the space of initial conditions. Using these transformations, the authors give a further classification of the 6 Painlevé equations related to some Dynkin diagrams, lists of folding transformations and diagrams are given. See also the second author [Jap. J. Math., New Ser. 5, 1--79 (1979; Zbl 0426.58017)] and the third author [Commun. Math. Phys. 220, 165--229 (2001; Zbl 1010.34083].
reviewed by: Günter Czichowski
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37K35
zbMATH DE Number: 2156242
zbMATH Keywords: Painlevé equation
zbMATH Keywords: folding transformation
zbMATH Keywords: symmetry
zbMATH Keywords: Bäcklund transformation
zbMATH Keywords: Dynkin diagram
MaRDI profile type: Publication
full work available at URL: s00208-004-0600-8
OpenAlex ID: W2068265109
cites work: Q4040877
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DOI: 10.1007/S00208-004-0600-8
description: scientific article; zbMATH DE number 2156242