Skip to main content
Log in

Convergence of Birkhoff normal forms for integrable systems

  • Published:
Commentarii Mathematici Helvetici

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. V. I. Arnold, Mathematical Methods in Classical Mechanics, Springer (1978).

  2. G. D. Birkhoff, Dynamical Systems AMS Colloquium Publ.IX (1927).

  3. H. Eliasson, Hamiltonian systems with Poisson commuting integrals, Thesis at Univ. of Stockholm (1984).

  4. S. Lang, Algebra, Addison-Wesley (1971).

  5. J. Moser,Stable and random motions in dynamical systems, Ann. Math. Studies77 Princeton Univ. Press (1973).

  6. J. Moser, Proof of a generalized form of a fixed point theorem due to G. D. Birkhoff, Lec. Notes in Math., Springer,597 (1977), 464–494.

    Google Scholar 

  7. J. Moser, Analytic surfaces in ℂ2 and their local hull of holomorphy, Annales Academiae Scientiarum Fenniae Ser. A. I.,10 (1985), 397–410.

    Google Scholar 

  8. H. Rüssmann,Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann.,154 (1964), 285–300.

    Article  MathSciNet  Google Scholar 

  9. C. L. Siegel,On integrals of canonical systems, Ann. Math.,42, (1941), 806–822.

    Article  Google Scholar 

  10. C. L. Siegel,Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichslösung, Math. Ann.,128, (1954), 144–170.

    Article  MathSciNet  Google Scholar 

  11. C. L. Siegel, andJ. K. Moser, Lectures on Celestial Mechanics, Springer (1971).

  12. J. Vey,Sur certain systèmes dynamiques séparables, Amer. J. Math.,100 (1978), 591–614.

    Article  MathSciNet  Google Scholar 

  13. S. L. Ziglin,Branching of solutions and nonexistence of first integrals in Hamiltonian mechanics I, Functional. Anal. Appl.16 (1983), 181–189.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ito, H. Convergence of Birkhoff normal forms for integrable systems. Commentarii Mathematici Helvetici 64, 412–461 (1989). https://doi.org/10.1007/BF02564686

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564686

Keywords

Navigation