Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution

The paper is devoted to non-Schlesinger isomonodromic deformations for resonant Fuchsian systems. There are very few explicit examples of such deformations in the literature. In this paper we construct a new example of the non-Schlesinger isomonodromic deformation for a resonant Fuchsian system of o...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2015
Main Authors: Bibilo, Y., Filipuk, G.
Format: Article
Language:English
Published: Інститут математики НАН України 2015
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147002
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution / Y. Bibilo, G. Filipuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Bibilo, Y.
Filipuk, G.
author_facet Bibilo, Y.
Filipuk, G.
citation_txt Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution / Y. Bibilo, G. Filipuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description The paper is devoted to non-Schlesinger isomonodromic deformations for resonant Fuchsian systems. There are very few explicit examples of such deformations in the literature. In this paper we construct a new example of the non-Schlesinger isomonodromic deformation for a resonant Fuchsian system of order 5 by using middle convolution for a resonant Fuchsian system of order 2. Moreover, it is known that middle convolution is an operation that preserves Schlesinger's deformation equations for non-resonant Fuchsian systems. In this paper we show that Bolibruch's non-Schlesinger deformations of resonant Fuchsian systems are, in general, not preserved by middle convolution.
first_indexed 2025-12-07T20:57:23Z
format Article
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id nasplib_isofts_kiev_ua-123456789-147002
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T20:57:23Z
publishDate 2015
publisher Інститут математики НАН України
record_format dspace
spelling Bibilo, Y.
Filipuk, G.
2019-02-12T18:15:54Z
2019-02-12T18:15:54Z
2015
Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution / Y. Bibilo, G. Filipuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 34M56; 44A15
DOI:10.3842/SIGMA.2015.023
https://nasplib.isofts.kiev.ua/handle/123456789/147002
The paper is devoted to non-Schlesinger isomonodromic deformations for resonant Fuchsian systems. There are very few explicit examples of such deformations in the literature. In this paper we construct a new example of the non-Schlesinger isomonodromic deformation for a resonant Fuchsian system of order 5 by using middle convolution for a resonant Fuchsian system of order 2. Moreover, it is known that middle convolution is an operation that preserves Schlesinger's deformation equations for non-resonant Fuchsian systems. In this paper we show that Bolibruch's non-Schlesinger deformations of resonant Fuchsian systems are, in general, not preserved by middle convolution.
Part of this work was carried out while Yu. Bibilo was visiting the Univerity of Warsaw in April
 2014. The authors acknowledge the support of the Polish NCN Grant 2011/03/B/ST1/00330.
 Yu. Bibilo also acknowledges the support of the Russian Foundation for Basic Research (grant
 no. RFBR 14-01-00346 A).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
Article
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spellingShingle Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
Bibilo, Y.
Filipuk, G.
title Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
title_full Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
title_fullStr Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
title_full_unstemmed Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
title_short Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
title_sort non-schlesinger isomonodromic deformations of fuchsian systems and middle convolution
url https://nasplib.isofts.kiev.ua/handle/123456789/147002
work_keys_str_mv AT bibiloy nonschlesingerisomonodromicdeformationsoffuchsiansystemsandmiddleconvolution
AT filipukg nonschlesingerisomonodromicdeformationsoffuchsiansystemsandmiddleconvolution