41
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

PRINCIPAL DIFFERENTIAL IDEALS AND A GENERIC INVERSE DIFFERENTIAL GALOIS PROBLEM FOR GLn

Pages 6071-6103 | Received 01 Aug 2001, Published online: 01 Sep 2006

REFERENCES

  • Adams, W.W.; Loustaunau, Ph. An Introduction to Gröbner Bases, Graduate Studies in Mathematics, American Mathematical Society, 1994
  • Albrecht , D.W. , Mansfield , E.L. and Milne , A.E. A 1996 . Algorithms for Special Integrals of Ordinary Differential Equations . J. Phys. , 29 ( 5 ) : 973 – 991 .
  • Beukers , F. and Heckmann , G. 1989 . Monodromy for the Hypergeometric Function . Invent. Math. , 95 : 325 – 354 .
  • Bialynicki-Birula , A. 1963 . On the Inverse Problem of Galois Theory of Differential Fields . Bull. Amer. Math. Soc. , 16 : 960 – 964 .
  • Boussel , K. 1989 . Groupes de Galois des e´quations hyperge´ome´triques . C.R. Acad. Sci. Paris., I , 309 : 587 – 589 .
  • Dodgson , C.L. 1866 . Condensation of Determinants . Proc. Royal Soc. London, , 15 : 150 – 155 .
  • Duval , A. and Loday-Richaud , M. 1992 . Kovacic's Algorithm and its Applications to Some Families of Special Functions . AAECC Journal , 3
  • Duval , A. and Mitschi , C. 1989 . Matrices de Stokes et Groupe de Galois des e´quations Hyperge´ome´triques Confluentes ge´ne´ralise´es . Pacific J. Math. , 138 : 25 – 56 .
  • Figueiredo , A. , Rocha-Filho , T.M. and Brenig , L. A 1999 . Necessary Conditions for the Existence of Quasi-polynomial Invariants: the Quasi-polynomial and Lotka-Volterra Systems . Phys. , 262 ( 1–2 ) : 158 – 180 .
  • Goldman , L. 1957 . Specialization and Picard–Vessiot Theory . Trans. Amer. Math. Soc. , 85 : 327 – 356 .
  • Juan, L. A Generic Picard–Vessiot Extension with Group and the Inverse Differential Galois Problem; Ph.D. Thesis, University of Oklahoma, 2000
  • Juan, L. Pure Picard–Vessiot Extensions with Generic Properties; (In preparation.)
  • Katz , N. 1987 . On the Calculation of Some Differential Galois Groups . Invent. Math. , 87 : 13 – 61 .
  • Kovacic , J. 1969 . The Inverse Problem in the Galois Theory of Differential Fields . Ann. of Math., , 89 : 583 – 608 .
  • Kovacic , J. 1971 . On the Inverse Problem in the Galois Theory of Differential Fields . Ann. of Math. , 93 : 269 – 284 .
  • Labrunie , S. A 1997 . On the Non-integrability of the Invariant Khler-Einstein Metrics . Phys. Lett. , 236 ( 5–6 ) : 439 – 444 .
  • Labrunie , S. 1996 . Simon On the Polynomial First Integrals of the Lotka-Volterra System . J. Math. Phys. , 37 ( 11 ) : 5539 – 5550 .
  • Maciejewski , A.J. and Strelcyn , J.-M. 1996 . Non-integrability of the Generalized Halphen System . Regul. Khaoticheskaya Din. , 1 ( 2 ) : 3 – 12 .
  • Magid, A. Lectures in Differential Galois Theory; University Lecture Series: American Mathematical Society, 1994
  • Miller, J. On Differentially Hilbertian Differential Fields; Ph.D. thesis, Columbia University, 1970
  • Mitschi , C. 1989 . Groupe de Galois des e´quations hyperge´ome´triques confluentes ge´ne´ralise´es . C.R. Acad. Sci. Paris. I , 309 : 217 – 220 .
  • Mitschi , C. 1996 . Differential Galois Groups of Generalized Hypergeometric Equations: An Approach Using Stokes Multipliers . Pacific J. Math. , 176 ( 2 ) : 365 – 405 .
  • Mitschi , C. and Singer , M.F. 1996 . Connected Linear Groups as Differential Galois Groups . J. Algebra, , 184 : 333 – 361 .
  • Noether , E. 1918 . Gleichungen mit vorgeschriebener Gruppen . Math. Ann. , 78 : 221 – 229 .
  • van der Put, M. Recent Work on Differential Galois Theory; Se´minaire BOURBAKI, 50e`me anne´e, 1997–1998, n 849
  • Ramis , J.-P. 1994 . “ Differential Equations, Dynamical Systems and Control Science ” . In About the Solution of Some Inverse Problems in Differential Galois Theory by Hamburger Equations Edited by: Elworthy , Everett and Lee . Vol. 157 , 277 – 300 . Lecture Notes in Pure and Applied Mathematics
  • Ramis , J.-P. 1996 . About the Inverse Problem in Differential Galois Theory: The Differential Abhyankar Conjecture Edited by: Braaksma , B.I.J. Singapore : World Scientific . The Stokes Phenomenon and Hilbert's 16th Problem
  • Robins , D.P. and Rumsey , H. Jr. 1986 . Determinants and Alternating Sign Matrices . Adv. in Math. , 62 : 169 – 184 .
  • Singer, M.F. Direct and Inverse Problems in Differential Galois Theory; Selected Works of Ellis Kolchin with Commentary, Bass, Buium, Cassidy Eds.; American Mathematical Society: 1999; 527–554
  • Singer , M.F. 1993 . Moduli of Linear Differential Equations on the Riemann Sphere with Fixed Galois Groups . Pacific J. Math. , 106 ( 2 ) : 343 – 395 .
  • Singer , M.F. and Ulmer , F. 1993 . Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations . Journal of Symbolic Comput. , 16 : 37 – 74 .
  • Tretkoff , C. and Tretkoff , M. 1979 . Solution of the Inverse Problem of Differential Galois Theory in the Classical Case . Amer. J. Math. , 101 : 1327 – 1332 .
  • Ulmer , F. and Weil , J.-A. 1996 . J . Symbolic Comput. , 28 ( 2 ) : 179 – 200 .
  • Weil, J.-A. Constantes et polynômes de Darboux en algèbre différentielle: Applications aux Systèmes Différentiels Linéaires; Ph.D. Thesis, École Polytechnique de France: 1995
  • Weil, J.-A. First Integrals and Darboux Polynomials of Homogeneous Linear Differential Systems. Applied Algebra, Algebraic Algorithms and Error-correcting Codes, Lecture Notes in Comput. Sci., 948, Springer: Berlin, 1995, 469–484

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.