A Root-Free Splitting-Lemma for Systems of Linear Differential Equations

by   Eckhard Pflügel, et al.
Kingston University

We consider the formal reduction of a system of linear differential equations and show that, if the system can be block-diagonalised through transformation with a ramified Shearing-transformation and following application of the Splitting Lemma, and if the spectra of the leading block matrices of the ramified system satisfy a symmetry condition, this block-diagonalisation can also be achieved through an unramified transformation. Combined with classical results by Turritin and Wasow as well as work by Balser, this yields a constructive and simple proof of the existence of an unramified block-diagonal form from which formal invariants such as the Newton polygon can be read directly. Our result is particularly useful for designing efficient algorithms for the formal reduction of the system.


page 1

page 2

page 3

page 4


On iterative methods based on Sherman-Morrison-Woodbury regular splitting

We consider a regular splitting based on the Sherman-Morrison-Woodbury f...

On Drinfel'd associators

In 1986, in order to study the linear representations of the braid group...

Exact splitting methods for kinetic and Schrödinger equations

In [8], some exact splittings are proposed for inhomogeneous quadratic d...

Linear Differential Equations as a Data-Structure

A lot of information concerning solutions of linear differential equatio...

Infinite matroids in tropical differential algebra

We consider a finite-dimensional vector space W⊂ K^E over an arbitrary f...

A Milstein-type method for highly non-linear non-autonomous time-changed stochastic differential equations

A Milstein-type method is proposed for some highly non-linear non-autono...

A Deforestation of Reducts: Refocusing

In a small-step semantics with a deterministic reduction strategy, refoc...

Please sign up or login with your details

Forgot password? Click here to reset