Isomonodromic deformations along a stratum of the coalescence locus

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.

59 pages, 4 figures

References in corpus (2)

• Isomonodromic Laplace Transform with Coalescing Eigenvalues and Confluence of Fuchsian Singularities
• Somonodromic Deformations Along the Caustic of a Dubrovin-Frobenius Manifold

Cited by in corpus (2)

• Asymptotic solutions for linear ODEs with not-necessarily meromorphic coefficients: a Levinson type theorem on complex domains, and applications
• Somonodromic Deformations Along the Caustic of a Dubrovin-Frobenius Manifold