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 |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| 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| _version_ | 1862569076232028160 |
|---|---|
| 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.
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| first_indexed | 2026-03-13T11:24:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212016 |
| 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 published earlier |
| 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 |
| work_keys_str_mv | AT vanderputmarius modulispacesforthefifthpainleveequation AT topjaap modulispacesforthefifthpainleveequation |