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 Mat. Zametki, 2007, Volume 81, Issue 4, Pages 599–613 (Mi mz3702)

General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems

V. A. Poberezhnyi

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: In contrast to nonresonance systems whose continuous deformations are always Schlesinger deformations, systems with resonances provide great possibilities for deformations. In this case, the number of continuous parameters of deformation, in addition to the location of the poles of the system, includes the data describing the Levelt structure of the system, or, in other words, the distribution of resonance directions in the space of solutions. The question of classifying the form and structure of deformations according to these parameters arises. In the present paper, we consider continuous isomonodromic deformations of Fuchsian systems, including those with respect to additional parameters, describe the corresponding linear problem, and present the Pfaff form of the linear problem of general continuous isomonodromic deformation of Fuchsian systems.

Keywords: Fuchsian equations and systems, isomonodromic deformation, Levelt normalization, gauge transformation, resonance singular point, Pfaff form

DOI: https://doi.org/10.4213/mzm3702

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English version:
Mathematical Notes, 2007, 81:4, 529–542

Bibliographic databases:

UDC: 517.9+514.745.8

Citation: V. A. Poberezhnyi, “General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems”, Mat. Zametki, 81:4 (2007), 599–613; Math. Notes, 81:4 (2007), 529–542

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz3702
• https://doi.org/10.4213/mzm3702
• http://mi.mathnet.ru/eng/mz/v81/i4/p599

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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. Poberezhny V., “On the Painlevé property of isomonodromic deformations of Fuchsian systems”, Acta Appl. Math., 101:1-3 (2008), 255–263
2. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33
3. R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Russian Math. Surveys, 66:1 (2011), 63–105
4. Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.
5. Davide Guzzetti, “Notes on Non-Generic Isomonodromy Deformations”, SIGMA, 14 (2018), 087, 34 pp.
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