Linear Differential Equations in the Complex Domain: Problems of Analytic Continuation

Projective isomonodromy and Galois groups

“…Therefore the Lax pair (3.4), (3.5) does not describe an isomonodromic deformation, since otherwise the coefficients of (3.5) would be rational (cf. [19], Remark A.5.2.5).…”

Microlocalization of subanalytic sheaves

“…We study the connection between specialization and microlocalization for subanalytic sheaves and the classical ones. Specialization of subanalytic sheaves generalize tempered and formal specialization of [1] and [6], in particular when we specialize Whitney holomorphic functions we obtain the sheaves of functions asymptotically developable of [20] and [29]. Moreover, thanks to the functor of microlocalization, we are able to generalize tempered and formal microlocalization introduced by Andronikof in [1] and Colin in [5] respectively.…”

Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems

“…3.6] for instance) when λ " p " 0. In the general case, it is sufficient to remark that [10] (see also [34,Thm. 3.3.1]): there exists a meromorphic gauge transformation Y " M ptqZ with M ptq P GL rn pCtturt´1sq that changes the r-reduced system (A) into a system ( M A) which is the companion form of a scalar linear differential equation Dyptq " 0 with polynomial coefficients, of order rn and levels ď 1 at the origin (the levels of D are the levels of (A)).…”