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arXiv · 1503.03959

Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution

Yulia Bibilo·Galina Filipuk
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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.

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Yulia Bibilo, Galina Filipuk. 2015-03-13. Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution. https://doi.org/10.3842/sigma.2015.023

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