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.
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
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\paper General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems
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\jour Math. Notes
\yr 2007
\vol 81
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\pages 529--542
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Linking options:
https://www.mathnet.ru/eng/mzm3702
https://doi.org/10.4213/mzm3702
https://www.mathnet.ru/eng/mzm/v81/i4/p599
This publication is cited in the following 6 articles:
Davide Guzzetti, “Notes on Non-Generic Isomonodromy Deformations”, SIGMA, 14 (2018), 087, 34 pp.
Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.
V. A. Poberezhny, “On deformations of linear systems of differential equations and the Painlevé property”, Journal of Mathematical Sciences, 195:4 (2012), 433–533
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
R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Russian Math. Surveys, 66:1 (2011), 63–105
Poberezhny V., “On the Painlevé property of isomonodromic deformations of Fuchsian systems”, Acta Appl. Math., 101:1-3 (2008), 255–263
Citation in format AMSBIB
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