### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 087, 34 pages      arXiv:1804.05688      https://doi.org/10.3842/SIGMA.2018.087
Contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev

### Notes on Non-Generic Isomonodromy Deformations

Davide Guzzetti
SISSA, Via Bonomea 265 - 34136 Trieste, Italy

Received April 17, 2018, in final form August 14, 2018; Published online August 21, 2018

Abstract
Some of the main results of [Cotti G., Dubrovin B., Guzzetti D., Duke Math. J., to appear, arXiv:1706.04808], concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are reviewed from the point of view of Pfaffian systems, making a distinction between weak and strong isomonodromic deformations. Such distinction has a counterpart in the case of Fuchsian systems, which is well known as Schlesinger and non-Schlesinger deformations, reviewed in Appendix A.

Key words: isomonodromy deformations; Stokes phenomenon; Pfaffian system; coalescing eigenvalues; Schlesinger deformations.

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