# 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} }

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

### Isomonodromic deformations along a stratum of the coalescence locus

- MathematicsJournal 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…

### On the universality of integrable deformations of solutions of degenerate Riemann-Hilbert-Birkhoff problems

- Mathematics
- 2021

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…

### Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities

- MathematicsLetters 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

### Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III

- Mathematics
- 1981

### Isomonodromic deformations of systems of linear differential equations with irregular singularities

- Mathematics
- 2012

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…

### Non-Schlesinger deformations of ordinary differential equations with rational coefficients

- Mathematics
- 2001

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…

### Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

- Mathematics
- 2006

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…

### Analytic geometry of semisimple coalescent Frobenius structures

- 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…

### Local Moduli of Semisimple Frobenius Coalescent Structures

- MathematicsSymmetry, 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,…

### ON ALMOST DUALITY FOR FROBENIUS MANIFOLDS

- Mathematics
- 2003

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…

### General linear problem of the isomonodromic deformation of Fuchsian systems

- Mathematics
- 2007

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…

### Deformations with a Resonant Irregular Singularity

- Mathematics
- 2017

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 \(z=\infty \)…

### Results on the extension of isomonodromy deformations to the case of a resonant irregular singularity

- MathematicsRandom 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 .],…