Skip to main content

Constrained equations; a study of implicit differential equations and their discontinuous solutions

Part of the Lecture Notes in Mathematics book series (LNM,volume 525)

Keywords

  • Variational Problem
  • Phase Portrait
  • Smooth Solution
  • Dense Subset
  • Integral Curve

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   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
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. R. Abraham, J. Robbin: Transversal mappings and flows, Benjamin Amsterdam, 1967.

    MATH  Google Scholar 

  2. V. I. Arnold: Normal forms of functions near degenerate critical points, Weyl groups Ak, Dk, Ek and Lagrange singularities. Functional Anal. and its Appl. Vol. 6, no. 4, (1972) 254–272.

    CrossRef  Google Scholar 

  3. J. M. Boardman: Singularities of differentiable maps, Publ. I.H.E.S., Vol. 33, (1967), 383–419.

    MathSciNet  MATH  Google Scholar 

  4. Th. Bröcker: Differentierbare Abbildungen, Der Regensburger Trichter band 3, Fachbereich Mathematik der Unversität Regensburg (B.R.D.).

    Google Scholar 

  5. J. Guckenheimer: Catastrophes and partial differential equations, Ann. de l’Institut Fourier XXIII, fas. 2, (1973), 31–59.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. E. Ihring: The regularization of non-linera electrical circuuits, to appear in B.A.M.S. (1974).

    Google Scholar 

  7. R.C. Robinson: Generic properties of conservative systems I, Amer. J. Math. 92 (1970), 562–603.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. S. Smale: Differential Dynamical Systems, B.A.M.S. 73 (1976), 747–817.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. S. Smale: On the mathematical foundations of electrical networks, J. Diff. Geometry. 7(19/2), 193–210.

    Google Scholar 

  10. F. Takens: Geometric aspects of non-linear R.L.C. networks, to appear in Warwick Dynamical Systems 1974.

    Google Scholar 

  11. R. Thom: Ensembles et Morphismes stratifies, B.A.M.S. 75 (1969), 240–284.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. Thom: L’évolution temporelle des catastrophes, in Applications of global analyses I, Mathematisch Instituut der Rijksuniversiteit Utrecht.

    Google Scholar 

  13. E. C. Zeeman: Differential equations for heartbeat and nerve impuls, in Dyn. Systems (ed. Peixoto), Acad. Press. New York, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Takens, F. (1976). Constrained equations; a study of implicit differential equations and their discontinuous solutions. In: Hilton, P. (eds) Structural Stability, the Theory of Catastrophes, and Applications in the Sciences. Lecture Notes in Mathematics, vol 525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077850

Download citation

  • DOI: https://doi.org/10.1007/BFb0077850

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07791-6

  • Online ISBN: 978-3-540-38254-6

  • eBook Packages: Springer Book Archive