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arXiv · 2111.02969

Isomonodromic deformations along a stratum of the coalescence locus

Davide Guzzetti
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Abstract

We consider deformations of a differential system with Poincare' rank 1 at infinity and Fuchsian singularity at zero along a stratum of a coalescence locus. We give necessary and sufficient conditions for the deformation to be strongly isomonodromic, both as an explicit Pfaffian system (integrable deformation) and as a non linear system of PDEs on the residue matrix A at the Fuchsian singularity. This construction is complementary to that of [13]. For the specific system here considered, the results generalize those of [26], by giving up the generic conditions, and those of [3], by giving up the Lidskii generic assumption. The importance of the case here considered originates form its applications in the study of strata of Dubrovin-Frobenius manifolds and F-manifolds.

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Davide Guzzetti. 2022-10-24. Isomonodromic deformations along a stratum of the coalescence locus. https://doi.org/10.1088/1751-8121%2Fac9ba8

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