Stokes phenomenon, multisummability and differential Galois groups

Michèle Loday-Richaud

Annales de l'institut Fourier (1994)

  • Volume: 44, Issue: 3, page 849-906
  • ISSN: 0373-0956

Abstract

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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 in a tannakian approach of differential Galois theory: in particular, we prove in this way, the theorem of Ramis on the generation of the differential Galois groups.

How to cite

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Loday-Richaud, Michèle. "Stokes phenomenon, multisummability and differential Galois groups." Annales de l'institut Fourier 44.3 (1994): 849-906. <http://eudml.org/doc/75083>.

@article{Loday1994,
abstract = {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 in a tannakian approach of differential Galois theory: in particular, we prove in this way, the theorem of Ramis on the generation of the differential Galois groups.},
author = {Loday-Richaud, Michèle},
journal = {Annales de l'institut Fourier},
keywords = {Stokes phenomenon; non-abelian cohomology; Stokes cocycle; summability; multisummability; differential Galois group; Tannakian method},
language = {eng},
number = {3},
pages = {849-906},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stokes phenomenon, multisummability and differential Galois groups},
url = {http://eudml.org/doc/75083},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Loday-Richaud, Michèle
TI - Stokes phenomenon, multisummability and differential Galois groups
JO - Annales de l'institut Fourier
PY - 1994
PB - Association des Annales de l'Institut Fourier
VL - 44
IS - 3
SP - 849
EP - 906
AB - 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 in a tannakian approach of differential Galois theory: in particular, we prove in this way, the theorem of Ramis on the generation of the differential Galois groups.
LA - eng
KW - Stokes phenomenon; non-abelian cohomology; Stokes cocycle; summability; multisummability; differential Galois group; Tannakian method
UR - http://eudml.org/doc/75083
ER -

References

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