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 |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| 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| _version_ | 1862748811866144768 |
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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.
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| 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 published earlier |
| 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 |