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Book Review

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Book Information:

Authors: Robert Bryant, Phillip Griffiths and Daniel Grossman
Title: Exterior differential systems and Euler-Lagrange partial differential equations
Additional book information: University of Chicago Press, 2003, 216 pp., ISBN 0-226-07793-4, $45.00, cloth; ISBN 0-226-07794-2, $17.00, paper

References [Enhancements On Off] (What's this?)

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  • 3. R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior differential systems, Mathematical Sciences Research Institute Publications, vol. 18, Springer-Verlag, New York, 1991. MR 1083148
  • 4. Carathéodory, C., Über die Variationsrechnung bei mehrfachen Integralen, Acta Sci. Mat. (Szeged), 4 (1929) 193-216.
  • 5. Cartan, É., Sur la structure des groupes infinis de transformations, Oeuvres Complètes, part. II, vol. 2, Gauthier-Villars, Paris, 1953, pp. 571-714. MR 0753095 (85g:01032b)
  • 6. Mark J. Gotay, An exterior differential systems approach to the Cartan form, Symplectic geometry and mathematical physics (Aix-en-Provence, 1990) Progr. Math., vol. 99, Birkhäuser Boston, Boston, MA, 1991, pp. 160–188. MR 1156539
  • 7. Griffiths, P.A., Exterior Differential Systems and the Calculus of Variations, Progress in Math. vol. 25, Birkhäuser, Boston, 1983. MR 0684663 (84h:58007)
  • 8. Ernst Hairer, Christian Lubich, and Gerhard Wanner, Geometric numerical integration, Springer Series in Computational Mathematics, vol. 31, Springer-Verlag, Berlin, 2002. Structure-preserving algorithms for ordinary differential equations. MR 1904823
  • 9. Martin Juráš and Ian M. Anderson, Generalized Laplace invariants and the method of Darboux, Duke Math. J. 89 (1997), no. 2, 351–375. MR 1460626, https://doi.org/10.1215/S0012-7094-97-08916-X
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  • 14. Peter J. Olver, Equivalence and the Cartan form, Acta Appl. Math. 31 (1993), no. 2, 99–136. MR 1223167, https://doi.org/10.1007/BF00990539
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  • 16. Wolfgang Reichel, Uniqueness theorems for variational problems by the method of transformation groups, Lecture Notes in Mathematics, vol. 1841, Springer-Verlag, Berlin, 2004. MR 2068382
  • 17. Tsujishita, T., On variational bicomplexes associated to differential equations, Osaka J. Math., 19 (1982) 311-363. MR 0667492 (84b:58105)
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Review Information:

Reviewer: Peter J. Olver
Affiliation: University of Minnesota
Journal: Bull. Amer. Math. Soc. 42 (2005), 407-412
MSC (2000): Primary 35A30, 58A15, 58E30
Published electronically: April 1, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society