# Isomonodromic deformations along a stratum of the coalescence locus

@article{Guzzetti2021IsomonodromicDA,
title={Isomonodromic deformations along a stratum of the coalescence locus},
author={Davide Guzzetti},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2021},
volume={55}
}
• D. Guzzetti
• Published 4 November 2021
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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 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 (Cotti et al 2019 Duke Math. J. 168 967–1108). For the…

## References

SHOWING 1-10 OF 32 REFERENCES

• 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,
• Mathematics
• 2021
We consider a 3-dimensional Pfaffian system, whose z-component is a differential system with irregular singularity at infinity and Fuchsian at zero. In the first part of the paper, we prove that its
We study the family of ordinary diﬀerential equations associated to a Dubrovin-Frobenius manifold along its caustic. Upon just loosing an idempotent at the caustic and under a non-degeneracy
The Hamiltonian structure of the monodromy preserving deformation equations of Jimboet al [JMMS] is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to
• D. Guzzetti
• Mathematics
Symmetry, Integrability and Geometry: Methods and Applications
• 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
A new class of isomonodromy equations will be introduced and shown to admit Kac–Moody Weyl group symmetries. This puts into a general context some results of Okamoto on the 4th, 5th and 6th Painlevé
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
• 2013
Let G be a complex, affine algebraic group and D a meromorphic connection on the trivial G-bundle over P^1, with a pole of order 2 at zero and a pole of order 1 at infinity. We show that the map S
• Mathematics
Duke Mathematical Journal
• 2019
We consider an $n\times n$ linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at $z=\infty$, holomorphically depending on parameter $t$ within a polydisc in $\mathbb{C}^n$
It is now twenty years since Jimbo, Miwa, and Ueno [23] generalized Schlesinger’s equations (governing isomonodromic deformations of logarithmic connections on vector bundles over the Riemann sphere)