Skip to main content

Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point

  • Chapter
  • 178 Accesses

Part of the book series: NATO ASI Series ((ASIC,volume 154))

Abstract

We restrict ourselves to the stability problems considered in our lecture because the length of this paper is limited. In contrast to the lecture, however, we consider here not only area preserving mappings but a more general class of mappings.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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. Birkhoff, G.D.: 1920, Acta Math. 43, p. 1

    Article  MathSciNet  MATH  Google Scholar 

  2. Cherry, T.M.: 1964, in Nonlinear Problems of Engineering (W.F. Ames Editor) Acad. Press, New York, p. 29

    Google Scholar 

  3. Cremer, H.: 1938, Math. Ann. 115, p. 573

    Article  MathSciNet  Google Scholar 

  4. Deprit, A. and A. Deprit-Bartholomé: 1967, Astron. J. 72, p. 173

    Article  ADS  Google Scholar 

  5. Markeev, A.P.: 1969, PMM 33, p. 112

    MathSciNet  MATH  Google Scholar 

  6. Rüssmann, H.: 1967, Math. Ann. 169, p. 55

    Article  MathSciNet  MATH  Google Scholar 

  7. Rüssmann, H.: 1977, ‘On the Convergence of Power Series Transformations of Analytic Mappings Near a Fixed Point into a Normal Form’, preprint IHES/M/77/178, Institut des Hautes Etudes Scientifique, Bures-sur-Yvette, France

    Google Scholar 

  8. Siegel, C.L. and J.K. Moser: 1971, Lectures on Celestial Mechanics, Springer-Verlag Berlin Heidelberg New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 D. Reidel Publishing Company

About this chapter

Cite this chapter

Rüssmann, H. (1985). Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point. In: Szebehely, V.G. (eds) Stability of the Solar System and Its Minor Natural and Artificial Bodies. NATO ASI Series, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5398-7_20

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-5398-7_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8883-1

  • Online ISBN: 978-94-009-5398-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics