# Notes on Non-Generic Isomonodromy Deformations

@article{Guzzetti2018NotesON,
title={Notes on Non-Generic Isomonodromy Deformations},
author={Davide Guzzetti},
journal={Symmetry, Integrability and Geometry: Methods and Applications},
year={2018}
}
• D. Guzzetti
• Published 16 April 2018
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications
Some of the main results of reference [12], 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 the Appendix.
3 Citations
• D. Guzzetti
• Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2022
We consider deformations of a differential system with Poincaré rank 1 at infinity and Fuchsian singularity at zero along a stratum of a coalescence locus. We give necessary and sufficient conditions
This paper addresses the classification problem of integrable deformations of solutions of “degenerate” Riemann–Hilbert–Birkhoff (RHB) problems. These consist of those RHB problems whose initial
• D. Guzzetti
• Mathematics
Letters in Mathematical Physics
• 2021
We consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters u=(u1,…,un)\documentclass[12pt]{minimal} \usepackage{amsmath}

## References

SHOWING 1-10 OF 42 REFERENCES

An isomonodromic deformation of a linear system of differential equations with irregular singularities is considered. A theorem on the general form of a differential 1-form describing such a
We consider deformations of 2×2 and 3×3 matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which do not satisfy the well known system of Schlesinger
We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is
• Mathematics
• 2017
We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in
• Mathematics
Symmetry, Integrability and Geometry: Methods and Applications
• 2020
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms,
We present a universal construction of almost duality for Frobenius man- ifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We
In contrast to nonresonance systems whose continuous deformations are always Schlesinger deformations, systems with resonances provide great possibilities for deformations. In this case, the number
I review topics of my talk in Alcala, inspired by the paper [1]. An isomonodromic system with irregular singularity at $$z=\infty$$ (and Fuchsian at $$z=0$$) is considered, such that $$z=\infty$$
• Mathematics
Random Matrices: Theory and Applications
• 2018
We explain some results of [G. Cotti, B. A. Dubrovin and D. Guzzetti, Isomonodromy deformations at an irregular singularity with coalescing eigenvalues, preprint (2017); arXiv:1706.04808 .],