Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution

Yulia Bibilo ; Galina Filipuk

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

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.

Détail

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

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