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Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
Інший ID:
2010 Mathematics Subject Classification: 34M56; 44A15
DOI:10.3842/SIGMA.2015.023
DOI:10.3842/SIGMA.2015.023
Посилання:
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.
Підтримка:
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).
Дата:
2015
Переглядів:
551
Завантажень:
242
Анотація:
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.
