Recent work on differential Galois theory

Marius Van der Put

Séminaire Bourbaki (1997-1998)

  • Volume: 40, page 341-367
  • ISSN: 0303-1179

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Van der Put, Marius. "Recent work on differential Galois theory." Séminaire Bourbaki 40 (1997-1998): 341-367. <http://eudml.org/doc/110252>.

@article{VanderPut1997-1998,
author = {Van der Put, Marius},
journal = {Séminaire Bourbaki},
keywords = {survey; inverse problem; differential Galois theory; Picard-Vessiot theory; differential Galois group; compact Riemann surface; classification of differential equations; field of convergent Laurent series},
language = {eng},
pages = {341-367},
publisher = {Société Mathématique de France},
title = {Recent work on differential Galois theory},
url = {http://eudml.org/doc/110252},
volume = {40},
year = {1997-1998},
}

TY - JOUR
AU - Van der Put, Marius
TI - Recent work on differential Galois theory
JO - Séminaire Bourbaki
PY - 1997-1998
PB - Société Mathématique de France
VL - 40
SP - 341
EP - 367
LA - eng
KW - survey; inverse problem; differential Galois theory; Picard-Vessiot theory; differential Galois group; compact Riemann surface; classification of differential equations; field of convergent Laurent series
UR - http://eudml.org/doc/110252
ER -

References

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  8. [H] J.E. Humphreys - Linear Algebraic Groups, Second edition, Springer Verlag, New York, 1981. Zbl0471.20029
  9. [H-P] P.A. Hendriks and M. van der Put - Galois action on solutions of a differential equation, Journal of Symbolic Computation19 (1995), no 6, 559-576. Zbl0855.12006
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  12. [Ka] N. Katz - Rigid Local Systems, Annals of Mathematical Studies, 1996 Zbl0864.14013
  13. [Ko] E.R. Kolchin - Differential Algebra and Algebraic Groups, Academic Press, New York, 1973. Zbl0264.12102
  14. [Kov] J.J. Kovacic - The inverse problem in the Galois theory of differential fields, Ann. of Math89 (1969), 583-608. Zbl0188.33801
  15. [Ma] A. Magid - Lectures on Differential Galois Theory, AMS University Lecture series 7, 1994. Zbl0855.12001
  16. [M-R1] J. Martinet and J.-P. Ramis - Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations (E. Tournier ed), Academic Press, 1989, 115-214. Zbl0722.12007
  17. [M-R2] J. Martinet and J.-P. Ramis - Elementary acceleration and multisummability -Annales de l'Institut Henri Poincaré, Physique Théorique54 (1991), no. 4, 331- 401. Zbl0748.12005
  18. [M-S1] C. Mitschi and M.F. Singer - Connected Linear Groups as Differential Galois Groups, Journal of Algebra184 (1996), 333 -361. Zbl0867.12004
  19. [M-S2] C. Mitschi and M.F. Singer - The inverse problem in differential Galois theory, The Stokes Phenomenon and Hilbert's 16th Problem (B.L.J. Braaksma et al ed.), World Scientific, River Edge, NJ, 1996, 185-197. Zbl0858.12003
  20. [M-S3] C. Mitschi and M.F. Singer - On Ramis' solution of the local inverse problem of differential Galois theory, Journal of Pure and Applied Algebra110 (1996), 185-194. Zbl0854.12001
  21. [P1] M. van der Put - Singular complex differential equations; An Introduction, Nieuw Archief voor Wiskunde, vierde serie 13 (1995), no. 3, 451-470. Zbl0860.34001
  22. [P2] M. van der Put - Symbolic analysis of differential equations, to appear in "Some Tapas of Computer Algebra" A.M. Cohen, H. Cuypers, H. Sterk eds., 1998. Zbl1002.12007
  23. [P3] M. van der Put - Galois theory of differential equations, Algebraic groups and Lie algebras, preprint Groningen, Sept 1997. 
  24. [R1] J.-P. Ramis - About the Inverse Problem in Differential Galois Theory: The Differential Abhyankar Conjecture, In "The Stokes Phenomenon and Hilbert's 16th Problem", World Scientific Publ. (Editors B.L.J. Braaksma, G.K. Immink, M. van der Put), Singapore1996. Zbl0860.12003
  25. [R2] J.-P. Ramis - About the Inverse Problem in Differential Galois Theory: The Differential Abhyankar Conjecture, Manuscript for Astérisque, version 16-1-1995. 
  26. [S] M.F. Singer - Direct and Inverse Problems in Differential Galois Theory, to be published in the introduction to Kolchin's collected works1998. 

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