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

Fuente: arXiv
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Autori principali: Dreyfus, Thomas, Heu, Viktoria
Natura: Preprint
Pubblicazione: 2020
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author Dreyfus, Thomas
Heu, Viktoria
author_facet Dreyfus, Thomas
Heu, Viktoria
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2005_12805
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation
Dreyfus, Thomas
Heu, Viktoria
Classical Analysis and ODEs
14D05, 14F35, 34M56, 39A13
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.
title Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation
topic Classical Analysis and ODEs
14D05, 14F35, 34M56, 39A13
url https://arxiv.org/abs/2005.12805