Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

Details Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

2005-06-16

arxiv.org/abs/math/0506328v1

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1007/s11040-005-9004-6

We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is isomonodromic if and only if the residue matrices satisfy the Schlesinger system with respect to the parameter. Without the non-resonance condition this result fails: there exist non-Schlesinger isomonodromic deformations. In the present article we introduce the class of the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal deformation is also an isomonodromic one. In general, the class of the isomonodromic deformations is much richer than the class of the isoprincipal deformations, but in the non-resonant case these classes coincide. We prove that a deformation is isoprincipal if and only if the residue matrices satisfy the Schlesinger system. This theorem holds in the general case, without any assumptions on the spectra of the residue matrices of the deformation. An explicit example illustrating isomonodromic deformations, which are neither isoprincipal nor meromorphic with respect to the parameter, is also given.

Affiliated with

Also associated with

No associations

Rating

Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-5211