Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution

作者：Bibilo Yulia^*; Filipuk Galina

来源：Symmetry Integrability and Geometry-Methods and Applications, 2015, 11: 023.

DOI：10.3842/SIGMA.2015.023

• Middle convolution
• isomonodromic deformation
• non-Schlesinger isomonodromic deformation

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.

• 出版日期2015