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On a differential equation arising in iteration theory in rings of formal power series in one variable

Part of the Lecture Notes in Mathematics book series (LNM,volume 1163)

Keywords

  • Abelian Group
  • Normal Form
  • Formal Power Series
  • Infinitesimal Generator
  • Analytic Iteration

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References

  1. Reich, L.: Analytische und fraktionelle Iteration formal-biholomorpher Abbildungen. Jahrbuch Überblicke der Mathematik, 123–144 (1979). Bibliographisches Institut 1979.

    Google Scholar 

  2. Reich, L.: Iteration problems in power series rings. In: Théorie de l'itération et ses applications, Toulouse, 17–22, Mai 1982. Colloques internationaux du CNRS, Paris 1982.

    Google Scholar 

  3. Targonski, Gy.: Topics in Iteration Theory. Vandenhoeck & Ruprecht, Göttingen 1981.

    Google Scholar 

  4. Jabotinsky, E.: Iteration. Doctoral Dissertation. The Hebrew University, Jerusalem, 1–120 (1955).

    Google Scholar 

  5. Jabotinsky, E.: Analytic iteration. Trans. AMS 108, 457–477 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Targonski, Gy.: New directions and open problems in iteration theory. Berichte der mathematisch-statistischen Sektion im Forschungszentrum Graz, Ber. Nr.229 (1984).

    Google Scholar 

  7. Beyer, W., and Channell, P.J.: A functional equation for the embedding of a homeomorphism of the interval into a flow. Lecture at the International Symposium on Iteration Theory and its Functional Equations, Lochau, Austria, 27.9.–2.10.1984.

    Google Scholar 

  8. Lewis, D.N.: On Formal Power Series Transformations. Duke Journal Math. 5, 794–805 (1939).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Sternberg, S.: Infinite Lie Groups and Formal Aspects of Dynamics. Journ. Math. Mech. 10, 451–474 (1961).

    MathSciNet  MATH  Google Scholar 

  10. Chen, K.T.: Local Diffeomorphisms-ℂ-Realizations of Formal Properties. American Journ. Math. 87, 140–157 (1965).

    CrossRef  Google Scholar 

  11. Reich, L., and Schwaiger, J.: Öber einen Satz von S. Sternberg in der Theorie der analytischen Iterationen. Monatsh. Math. 83, 207–221 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Reich, L., and Schwaiger, J.: Eine Linearisierungsmethode für Funktionalgleichungen vom iterativen Typus in Potenzreihenringen. Aequationes Math. 20, 224–243 (1980).

    CrossRef  MathSciNet  Google Scholar 

  13. Birkhoff, G.D.: Surface Transformations and their Dynamical Applications. Acta Math. 43, 1–119.

    Google Scholar 

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© 1985 Springer-Verlag

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Reich, L. (1985). On a differential equation arising in iteration theory in rings of formal power series in one variable. In: Liedl, R., Reich, L., Targonski, G. (eds) Iteration Theory and its Functional Equations. Lecture Notes in Mathematics, vol 1163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076427

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  • DOI: https://doi.org/10.1007/BFb0076427

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16067-0

  • Online ISBN: 978-3-540-39749-6

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