On the monodromy of the deformed cubic oscillator

We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Inve...

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Autores principales: Bridgeland, Tom, Masoero, Davide
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9889533/
https://www.ncbi.nlm.nih.gov/pubmed/36744240
http://dx.doi.org/10.1007/s00208-021-02337-w
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author Bridgeland, Tom
Masoero, Davide
author_facet Bridgeland, Tom
Masoero, Davide
author_sort Bridgeland, Tom
collection PubMed
description We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Invent Math 216(1):69–124, 2019) arising from the Donaldson-Thomas theory of the A[Formula: see text] quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.
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spelling pubmed-98895332023-02-02 On the monodromy of the deformed cubic oscillator Bridgeland, Tom Masoero, Davide Math Ann Article We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Invent Math 216(1):69–124, 2019) arising from the Donaldson-Thomas theory of the A[Formula: see text] quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map. Springer Berlin Heidelberg 2022-01-04 2023 /pmc/articles/PMC9889533/ /pubmed/36744240 http://dx.doi.org/10.1007/s00208-021-02337-w Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Bridgeland, Tom
Masoero, Davide
On the monodromy of the deformed cubic oscillator
title On the monodromy of the deformed cubic oscillator
title_full On the monodromy of the deformed cubic oscillator
title_fullStr On the monodromy of the deformed cubic oscillator
title_full_unstemmed On the monodromy of the deformed cubic oscillator
title_short On the monodromy of the deformed cubic oscillator
title_sort on the monodromy of the deformed cubic oscillator
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9889533/
https://www.ncbi.nlm.nih.gov/pubmed/36744240
http://dx.doi.org/10.1007/s00208-021-02337-w
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