Integrable deformations and degenerations of some irregular singularities

TL;DR

This paper extends Malgrange's results on integrable deformations of irregular singularities to degenerate cases, with applications to Birkhoff problems and Frobenius manifold construction.

Contribution

It introduces a generalized framework for integrable deformations of irregular singularities, including degenerate cases, expanding the scope of previous theories.

Findings

Extended Malgrange's theorem to degenerate irregular singularities

Applied results to Birkhoff problem solutions

Constructed Frobenius manifolds from deformed irregular singularities

Abstract

Inspired by an article of Cotti, Dubrovin and Guzzetti arXiv:1706.04808, we extend to a degenerate case a result of Malgrange on integrable deformations of irregular singularities. We give an application to integrable deformations of the solution of some Birkhoff problem and apply it to the construction of Frobenius manifolds.