Some applications of the parameterized Picard-Vessiot theory
This expository paper presents some applications of the parameterized Picard-Vessiot theory for ordinary differential equations, mainly related to monodromy.
math.CA↗
arXiv subjects
Claude Mitschi
Publications and source records attributed to Claude Mitschi.
Projective Isomonodromy and Galois Groups
In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy evolving deformation of linear differential equations, based on the example of the Darboux-Halphen equation. We give an algebraic condition for a paramaterized linear differential equation to be projectively isomonodromic, in terms of the derived group of its parameterized Picard-Vessiot group.
math.CA↗
Monodromy groups of parameterized linear differential equations with regular singularities
We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the weak Riemann-Hilbert Problem and a special case of the inverse problem in parameterized Picard-Vessiot theory.
math.CA↗
On the Constructive Inverse Problem in Differential Galois Theory
We give sufficient conditions for a linear differential equation to have a given semisimple group as its Galois group. For any linear algebraic group G given as a semidirect product of a finite subgroup and a normal subgroup that is a product of groups of type An, Cn, Dn, E6, or E7, we construct a differential equation over C(x) having Galois group G.
math.GM↗