Integrable Deformations and Degenerations of Some Irregular Singularities

Abstract

We extend to a degenerate case a result by B. Malgrange on integrable deformations of irregular singularities, inspired by Cotti, Dubrovin and Guzzetti (Local moduli of semisimple Frobenius coalescent structures, SIGMA Symmetry Integrability Geom. Methods Appl. 16 (2020), paper no. 040). We give an application to integrable deformations of some meromorphic connections in Birkhoff normal form and to the construction of Frobenius manifolds.