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SIGMA, 2015, Volume 11, 023, 14 pages (Mi sigma1004)  

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

Abstract: 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.

Keywords: Middle convolution; isomonodromic deformation; non-Schlesinger isomonodromic deformation.

DOI: https://doi.org/10.3842/SIGMA.2015.023

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Full text: http://www.emis.de/journals/SIGMA/2015/023/
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Bibliographic databases:

ArXiv: 1503.03959
Document Type: Article
MSC: 34M56; 44A15
Received: November 20, 2014; in final form March 4, 2015; Published online March 13, 2015
Language: English

Citation: Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.

Citation in format AMSBIB
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\by Yulia~Bibilo, Galina~Filipuk
\paper Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and~Middle Convolution
\jour SIGMA
\yr 2015
\vol 11
\papernumber 023
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma1004}
\crossref{https://doi.org/10.3842/SIGMA.2015.023}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925003012}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bibilo Yu., Filipuk G., “Middle Convolution and Non-Schlesinger Deformations”, Proc. Jpn. Acad. Ser. A-Math. Sci., 91:5 (2015), 66–69  crossref  mathscinet  zmath  isi  scopus
    2. Mitschi, C., “Inverse problems, in: Divergent Series, Summability and Resurgence I”, Lecture Notes in Mathematics, 2153, 2016, 75-86  crossref  mathscinet
  • Symmetry, Integrability and Geometry: Methods and Applications
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