Skip to main content

Normal forms for deterministic and stochastic systems

  • 1003 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1331)

Abstract

A global characterization for the nonlinear terms of the normal form of singular vector fields is discussed. Generalizations to periodic and stochastic perturbations are also presented.

Keywords

  • Normal Form
  • Center Manifold
  • Negative Real Part
  • Marginal Part
  • Stochastic Perturbation

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   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
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. P. Coullet, E.A. Spiegel, SIAM J. Appl. Math. 43, 774 (1983).

    CrossRef  MathSciNet  Google Scholar 

  2. C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet, G. Iooss, A simple global characterization for normal forms of singular vector fields, preprint Univ. Nice NTH 86/6, to appear in Physica D.

    Google Scholar 

  3. V. Arnold, Chapitres supplémentaires de la théorie des équations differentielles ordinaires, ed. MIR, Mosou (1980).

    Google Scholar 

  4. V. Bargmann, Comm. Pure Applied Math. 14, 187 (1961).

    CrossRef  MathSciNet  Google Scholar 

  5. C. Elphick, G. Iooss, E. Tirapegui, Phys. Lett. 120A, 459 (1987).

    CrossRef  MathSciNet  Google Scholar 

  6. P. Coullet, C. Elphick, E. Tirapegui, Phys. Lett. 111A, 277 (1985).

    CrossRef  MathSciNet  Google Scholar 

  7. F. Baras, P. Coullet, E. Tirapegui, J. Stat. Phys. 45, 745 (1986).

    CrossRef  MathSciNet  Google Scholar 

  8. C. Elphick, E. Tirapegui, in Instabilities and Nonequilibrium Structures, eds. E. Tirapegui and D. Villarroel (Reidel, 1987).

    Google Scholar 

  9. O. Descalzi, C. Elphick, E. Tirapegui, in preparation.

    Google Scholar 

  10. N.G. van Kampen, Stochastic processes in physics and chemistry, Chapter VIII 6, North-Holland (1984).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Triapegui, E. (1988). Normal forms for deterministic and stochastic systems. In: Bamón, R., Labarca, R., Palis, J. (eds) Dynamical Systems Valparaiso 1986. Lecture Notes in Mathematics, vol 1331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083076

Download citation

  • DOI: https://doi.org/10.1007/BFb0083076

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50016-2

  • Online ISBN: 978-3-540-45889-0

  • eBook Packages: Springer Book Archive