Skip to main content

Complete integrability with noncommuting integrals of certain euler equations

  • 269 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1214)

Keywords

  • Euler Equation
  • Weyl Group
  • Cartan Subalgebra
  • Semisimple Element
  • Noncommuting Integral

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnol’d V.I. Mathematical Methods of Classical Mechanics. Springer-Verlag, 1978.

    Google Scholar 

  2. Manakov S.V. Remarks on the integrability of Euler equations of the n-dimensional spinning top. Funct.Analys i Prilozen., 1976, V.10, No 4, p.93–94 (in Russian).

    MathSciNet  Google Scholar 

  3. Nehoroshev N.N. Action-angle variables and their generalization. Trudy Moscow Math.Obchestva, 1972, V.24, p.181–198 (in Russian).

    Google Scholar 

  4. Mishchenko A.S., Fomenko A.T. The generalized Liouville method of integration of Hamiltonian systems.-Func. Anal. i Prilozen., 1978, v.12, No 2, p.46–56 (in Russian).

    MathSciNet  MATH  Google Scholar 

  5. Mischchenko A.S., Fomenko A.T. The integration of the Hamiltonian systems with noncommutting symmetries. In: Trudy Seminara po Vect. and Tens.Anal., V.20. Moscow, Mosc.Univ.Press, 1981, p.5–54. (in Russian)

    Google Scholar 

  6. Mishchenko A.S., Fomenko A.T. Euler’s equations on finite-dimensional Lie groups.-Izv.Acad.Nayk SSSR, Ser.Math., 1978, v.42, No 2, p.396–415. (in Russian)

    MATH  Google Scholar 

  7. Mishchenko A.S., Fomenko A.T. The integrability of the Euler’s equation on the semisimple Lie algebras. In: Trudy Seminara po Vect. i Tenz.Anal., v.19, Moscow, Moscow Univ.Press, 1979, p.3–94 (in Russian).

    Google Scholar 

  8. Dao Chong Thi (Dào Trong Thi). The integrability of Euler Equations on the homogeneous symplectic manifolds.-Mat.Sb., 1979, v.106, No 2, p.154–161 (in Russian).

    MathSciNet  Google Scholar 

  9. Mishchenko A.S. The integration of the geodesic flows on symmetric spaces.-Math.Zametki, 1982, v.31, No 2, p.257–262 (in Russian).

    MathSciNet  MATH  Google Scholar 

  10. Helgason S. Differential Geometry and Symmetric Spaces. Academic Press, N.Y and London, 1962.

    MATH  Google Scholar 

  11. Bourbaki N. Groupes et algèbres de Lie, Chap.IY-YI. Hermann, Paris, 1968.

    Google Scholar 

  12. Diximier J. Algèbres enveloppantes. Gauthier-Villars, Paris, 1974

    Google Scholar 

  13. Trofimov V.V. Finite-dimensional representations of Lie algebras and completely integrable systems.-Math.Sbornik, 1980, v.111, No 4, p.610–621 (in Russian).

    MathSciNet  Google Scholar 

  14. Kostant B. The solution to a generalized Toda lattice and representation theory.-Adv. in Math., 1980, 34:3, p.195–338.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Brailov A.V. Some cases of complete integrability of the Euler equations and applications.-Doklady AN SSSR, 1983, v.268, No 5, p.1043–1046 (in Russian).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this chapter

Cite this chapter

Brailov, A.V. (1986). Complete integrability with noncommuting integrals of certain euler equations. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications II. Lecture Notes in Mathematics, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075957

Download citation

  • DOI: https://doi.org/10.1007/BFb0075957

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16821-8

  • Online ISBN: 978-3-540-47084-7

  • eBook Packages: Springer Book Archive