Moduli Spaces for the Fifth Painlevé Equation

Isomonodromy for the fifth Painlevé equation P₅ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlevé spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for P₅...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2023
Hauptverfasser: van der Put, Marius, Top, Jaap
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2023
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212016
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Moduli Spaces for the Fifth Painlevé Equation. Marius van der Put and Jaap Top. SIGMA 19 (2023), 068, 26 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author van der Put, Marius
Top, Jaap
author_facet van der Put, Marius
Top, Jaap
citation_txt Moduli Spaces for the Fifth Painlevé Equation. Marius van der Put and Jaap Top. SIGMA 19 (2023), 068, 26 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Isomonodromy for the fifth Painlevé equation P₅ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlevé spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for P₅, introduced by Noumi-Yamada et al., is shown to be induced by a natural fine moduli space of connections of rank 4. As a by-product, one obtains a polynomial Hamiltonian for P₅, equivalent to the one of Okamoto.
first_indexed 2026-03-13T11:24:22Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-13T11:24:22Z
publishDate 2023
publisher Інститут математики НАН України
record_format dspace
spelling van der Put, Marius
Top, Jaap
2026-01-22T09:18:47Z
2023
Moduli Spaces for the Fifth Painlevé Equation. Marius van der Put and Jaap Top. SIGMA 19 (2023), 068, 26 pages
1815-0659
2020 Mathematics Subject Classification: 33E17; 14D20; 14D22; 34M55
arXiv:2107.07204
https://nasplib.isofts.kiev.ua/handle/123456789/212016
https://doi.org/10.3842/SIGMA.2023.068
Isomonodromy for the fifth Painlevé equation P₅ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlevé spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for P₅, introduced by Noumi-Yamada et al., is shown to be induced by a natural fine moduli space of connections of rank 4. As a by-product, one obtains a polynomial Hamiltonian for P₅, equivalent to the one of Okamoto.
We are indebted to the referees of earlier versions of this manuscript for their careful reading and for the useful suggestions and questions they provided. One referee suggested that the construction of our moduli spaces could result in non-separated spaces. This problem has f inally, after additional comments from the same referee, been solved by a small restriction on the parameters, a “natural” restriction on the set of reducible differential modules in the sets S(θ₀, θ₁, θ∞) and corresponding restrictions for the spaces ᵍᵉᵒᵐ(θ₀, θ₁, θ∞) and ℳ(θ₀, θ₁, θ∞).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Moduli Spaces for the Fifth Painlevé Equation
Article
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spellingShingle Moduli Spaces for the Fifth Painlevé Equation
van der Put, Marius
Top, Jaap
title Moduli Spaces for the Fifth Painlevé Equation
title_full Moduli Spaces for the Fifth Painlevé Equation
title_fullStr Moduli Spaces for the Fifth Painlevé Equation
title_full_unstemmed Moduli Spaces for the Fifth Painlevé Equation
title_short Moduli Spaces for the Fifth Painlevé Equation
title_sort moduli spaces for the fifth painlevé equation
url https://nasplib.isofts.kiev.ua/handle/123456789/212016
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