Skip to main content
SpringerLink
Log in

Geometry of jet bundles and the structure of lagrangian and hamiltonian formalisms

  • Conference paper
  • First Online:
Geometric Methods in Mathematical Physics

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. A.M. Vinogradov, Many-valued solutions, and a principle for the classification of nonlinear differential equations, Soviet Math. Dokl. 14(1973), 661–665.

    MATH  Google Scholar 

  2. A.M. Vinogradov, I.S. Krasil'shchik, What is the Hamiltonian formalism? Russian Math. Surveys, 30:1(1975), 177–202.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. A.M. Vinogradov, B.A. Kupershmidt, The structures of Hamiltonian mechanics, Russian Math. Surveys, 32:4(1977), 177–243.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. B.A. Kupershmidt, On geometry of jet manifolds, Uspekhi Math. Nauk 30:5(1975), 211–212.

    MathSciNet  Google Scholar 

  5. B.A. Kupershmidt, The Lagrangian formalism in the calculus of variations, Func. Anal. Appl. 10(1976), 147–149.

    Article  MathSciNet  Google Scholar 

  6. V.V. Lychagin, Local classification of nonlinear first order partial differential equations, Russian Math. Surveys 30:1(1975), 105–175.

    Article  ADS  Google Scholar 

  7. Whatever about singularities of smooth maps.

    Google Scholar 

  8. H. Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. Math. (2), 86(1967), 246–270.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Goldschmidt, Integrability criteria for systems of non-linear partial differential equations, J. Diff. Geometry 1(1967), 269–307.

    MathSciNet  MATH  Google Scholar 

  10. R. Hermann, Currents in classical field theories, J. Math. Phys. 13:1(1972), 97–99.

    Article  ADS  MathSciNet  Google Scholar 

  11. Krupka, Lagrange theory in fibered manifolds, Reports Math. Phys. 2(1971) 121–133.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. J. Sniatycki, On the geometric structure of classical field theory in Lagrangian formulation, Proc. Cambr. Phil. Soc. 68:2(1970), 475–484.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. H. Goldschmidt, S. Sternberg, The Hamilton-Cartan formalism in the calculus of variations, Ann. Inst. Fourier, Grenoble 23(1973), 203–267.

    Article  MathSciNet  MATH  Google Scholar 

  14. L.J.F. Broer, J.A. Kobussen, Canonical transformations and generating functionals, Phisica 62(1972), 275–288.

    Article  ADS  MathSciNet  Google Scholar 

  15. B.A. Kupershmidt, Yu. I. Manin, Equations of long waves with a free surface II, Hamiltonian structure and higher equations, Func. Anal. Appl. 12(1978), 20–29.

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu. I. Manin, Algebraic aspects of nonlinear differential equations, J. Sov. Math, (1979), 1–122.

    Google Scholar 

Download references

Authors
  1. B. A. Kupershmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Gerald Kaiser Jerrold E. Marsden

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Kupershmidt, B.A. (1980). Geometry of jet bundles and the structure of lagrangian and hamiltonian formalisms. 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/BFb0092026

Download citation

  • DOI: https://doi.org/10.1007/BFb0092026

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09742-6

  • Online ISBN: 978-3-540-38571-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation