Skip to main content

Generalizations of some theorems of small divisors to non archimedean fields

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1007))

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   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Amice, Les nombres p-adiques, Presses Universitaires de France, Paris, 1975.

    MATH  Google Scholar 

  2. V.I. Arnold, Small denominators I, Mappings of circumference onto itself, Amer. Math. Soc. Transl. Ser. 2, 46 pp. 213–284.

    Google Scholar 

  3. M.R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. I.H.E.S. 49 pp. 5–233.

    Google Scholar 

  4. E. Lutz, Sur les approximations diophantiennes linéaires p-adiques, Hermann, Paris, 1955.

    MATH  Google Scholar 

  5. K. Mahler, P-adic numbers and their functions, Camb. Univ. Press, Cambridge, second edition, 1981.

    MATH  Google Scholar 

  6. K. Meyer, The implicit function theorem and analytic differential equations, Springer Lect. Notes in Math. 468, Proc. Symp. on Dynamical Systems at Warwick (1974).

    Google Scholar 

  7. A.C.M. Van Rooij, Non archimedean function analysis, Marcel Dekker, New York, 1978.

    MATH  Google Scholar 

  8. H. Rűssmann, Kleine Nenner II: Bemerkungen zur Newton'schen Methode. Nachr. Akad. Wiss. Gőttingen Math. Phys. K1. (1972) pp. 1–20.

    Google Scholar 

  9. W.H. Schikhof, Non archimedean calculus, Lecture notes, Nijmegean, Katholieke Univ., 1978.

    Google Scholar 

  10. J.P. Serre, Lie algebras and Lie groups, Benjamin, New York, 1965.

    MATH  Google Scholar 

  11. Y. Sibuya & S. Sperber, Convergence of power series of p-adic non linear differential equations, preprint Univ. Minnesota (1978).

    Google Scholar 

  12. C.L. Siegel, Iteration of analytic functions, Ann. Math. 43 (1942), pp. 607–612.

    Article  MathSciNet  MATH  Google Scholar 

  13. C.L. Siegel, Űber die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichawichtslösung, Nachr. Akad. Wiss. Gőttingen, Math. Phys. K. (1952), pp. 21–30.

    Google Scholar 

  14. C.S. Weisman, On p-adic differentiability, J. Number th. 9 (1977), pp. 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  15. E. Zehnder, A simple proof of a generalization of a theorem by C.L. Siegel, Lec. Notes in Math. 597, Springer-Verlag, Berlin, (1977), pp. 855–866.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. Palis Jr.

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Herman, M., Yoccoz, J.C. (1983). Generalizations of some theorems of small divisors to non archimedean fields. In: Palis, J. (eds) Geometric Dynamics. Lecture Notes in Mathematics, vol 1007. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061427

Download citation

  • DOI: https://doi.org/10.1007/BFb0061427

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12336-1

  • Online ISBN: 978-3-540-40969-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics