Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation

In the current paper we study the \(q\)-analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a \(q\)-analogue of Schlesinger equations and show that for a convenient change of variables and auxiliary parameters, it admits a...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Dreyfus, Thomas, Heu, Viktoria
Format: Article
Language:English
Subjects:
Degeneration
Differential equations
Initial conditions
Online Access:Get full text
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Summary:In the current paper we study the \(q\)-analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a \(q\)-analogue of Schlesinger equations and show that for a convenient change of variables and auxiliary parameters, it admits a \(q\)-analogue of Hamiltonian formulation. This allows us to show that Sakai's \(q\)-analogue of Okamoto space of initial conditions for \(qP_\mathrm{VI}\) admits the differential Okamoto space \emph{via} some natural limit process.
ISSN:2331-8422
DOI:10.48550/arxiv.2005.12805