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Involution theorems

Part of the Lecture Notes in Mathematics book series (LNM,volume 775)

Keywords

  • Hamiltonian System
  • Poisson Bracket
  • Symplectic Structure
  • Hamiltonian Structure
  • Toda Lattice

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Bibliography

  1. R. Abraham, J. Marsden: Foundations of Mechanics, Benjamin/Cummings, 1978.

    Google Scholar 

  2. M. Adler: On a trace functional for formal pseudo-differential operators and the symplectic structure of the KortewegdeVries equations, Inventions Math, 1979.

    Google Scholar 

  3. M. Adler, P. van Moerkbeke: Algebraic curves and the classical Katz-Moody algebras, preprint, 1979.

    Google Scholar 

  4. M. Adler, J. Moser: preprint on the geodesic problem on the ellipsoid and the Neumann problem, 1979.

    Google Scholar 

  5. I.M. Gelfand, L.A. Dikii: The resolvent and Hamiltonian systems, Funct. Anal. and its Applications 11, 11–27, 10, 1977.

    MathSciNet  Google Scholar 

  6. R. Jost: Poisson brackets (an unpredagogical lecture), Rev. Mod. Phys. 36, 572–579, 1964.

    CrossRef  ADS  Google Scholar 

  7. D. Kazhdan, B. Kostant, S. Sternberg: Hamiltonian group actions and dynamical systems of Calogerotype, Comm. Pure Appl. Math, 31 (1978) 481–568.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. B. Kostant: The solution to a generalized Toda lattice and representation theory, preprint, MIT, 1979.

    Google Scholar 

  9. B. Kupershmidt: Deformations of Hamiltonian structures, prinprint, MIT, 1979.

    Google Scholar 

  10. B. Kupershmidt, Yu. Manin: Equations of long waves with a free surface, Funkts. Analiz. Prilozhen., 11, No. 3, 31–42, 1977.

    MathSciNet  Google Scholar 

  11. Yu, Manin: Algebraic aspects of non-linear differential equations, Journal of Soviet Math., Vol. 11, No. 1, 1–122, 1979.

    CrossRef  ADS  MATH  Google Scholar 

  12. J. Marsden, A. Weinstein: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5, 121–130, 1974.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  13. A.S. Mishchenko, A.T. Fomenko: Euler equations on finite dimensional Lie groups, Math. USSR, Izvestija, Vol. 12, No. 2, 371–389, 1978.

    CrossRef  ADS  MATH  Google Scholar 

  14. J. Moser: Various aspects of integrable Hamiltonian systems, C.I.M.E., Bressanone, 1978.

    MATH  Google Scholar 

  15. T. Ratiu: The motion of the free n-dimensional rigid body, preprint, Berkeley, 1979.

    Google Scholar 

  16. T. Ratiu: Euler-Poisson equations on Lie algebras and the generalized Lagrange top, preprint, Berkeley, 1979.

    Google Scholar 

  17. W. Symes: On systems of Toda, type, MRC Technical Summary Report, #1957, University of Wisconsin-Madison, 1979.

    Google Scholar 

  18. W. Symes: Relations among generalized Korteweg-deVries systems, J. Math. Phys. 20 (4), April 1979.

    Google Scholar 

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© 1980 Springer-Verlag

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Ratiu, T. (1980). Involution theorems. In: Kaiser, G., Marsden, J.E. (eds) Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092027

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  • DOI: https://doi.org/10.1007/BFb0092027

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09742-6

  • Online ISBN: 978-3-540-38571-4

  • eBook Packages: Springer Book Archive