We consider deformations of a differential system with Poincaré rank 1 at infinity and Fuch-sian 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 de- formation) 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.

Isomonodromic deformations along a stratum of the coalescence locus / Guzzetti, Davide. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:45(2022), pp. 1-59. [10.1088/1751-8121/ac9ba8]

Isomonodromic deformations along a stratum of the coalescence locus

Davide Guzzetti
2022-01-01

Abstract

We consider deformations of a differential system with Poincaré rank 1 at infinity and Fuch-sian 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 de- formation) 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.
55
45
1
59
455202
10.1088/1751-8121/ac9ba8
Guzzetti, Davide
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/130130
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