SIGMA, 2015, Volume 11, 023, 14 pages
This article is cited in 2 scientific papers (total in 2 papers)
Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
Yulia Bibiloa, Galina Filipukb
a Department of Theory of Information Transmission and Control, Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, 127994, Russia
b Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, Warsaw, 02-097, Poland
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.
Middle convolution; isomonodromic deformation; non-Schlesinger isomonodromic deformation.
PDF file (351 kB)
MSC: 34M56; 44A15
Received: November 20, 2014; in final form March 4, 2015; Published online March 13, 2015
Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.
Citation in format AMSBIB
\by Yulia~Bibilo, Galina~Filipuk
\paper Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and~Middle Convolution
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This publication is cited in the following articles:
Bibilo Yu., Filipuk G., “Middle Convolution and Non-Schlesinger Deformations”, Proc. Jpn. Acad. Ser. A-Math. Sci., 91:5 (2015), 66–69
Mitschi, C., “Inverse problems, in: Divergent Series, Summability and Resurgence I”, Lecture Notes in Mathematics, 2153, 2016, 75-86
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