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Stokes phenomenon, multisummability and differential Galois groups

Michèle Loday-Richaud (1994)

Annales de l'institut Fourier

We precise the cohomological analysis of the Stokes phenomenon for linear differential systems due to Malgrange and Sibuya by making a rigid natural choice of a unique cocycle (called a Stokes cocyle) in every cohomological class. And we detail an algebraic algorithm to reduce any cocycle to its cohomologous Stokes form. This gives rise to an almost algebraic definition of sums for formal solutions of systems which we compare to the most usual ones. We also use this construction to the Stokes cocycle...

Substitution method for generalized linear differential equations

Dana Fraňková (1991)

Mathematica Bohemica

The generalized linear differential equation d x = d [ a ( t ) ] x + d f where A , f B V n l o c ( J ) and the matrices I - Δ - A ( t ) , I + Δ + A ( t ) are regular, can be transformed d y d s = B ( s ) y + g ( s ) using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.

Currently displaying 41 – 60 of 77