Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A note on the parameters of rational iteration groups

  • 18 Accesses


The note presents some facts on the relations between rational iteration groups and the corresponding parameter sets.

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


  1. [1]

    Abel, U.,On the group of piecewise linear monotone bijections of an arc. Math. Z.171 (1980), 155–161.

  2. [2]

    Abel, U.,A homeomorphism of Q with Q as an orbit. Elem. Math.37 (1982), 108–109.

  3. [3]

    Abel, U.,Sur les groupes d'itération monotones. Publ. Math. Debrecen29 (1982), 65–71.

  4. [4]

    Aczél, J., Kalmár, L. andMikusiński, J. G.,Sur l'équation de translation. Studia Math.12 (1951), 112–116.

  5. [5]

    Berg, L.,Iterationen von beliebiger Ordnung. Z. Angew. Math. Mech.40 (1960), 215–229.

  6. [6]

    Berg, L.,Unstetige, monotone Iterationsgruppen reeller Funktionen. Publ. Math. Debrecen9 (1862), 47–56.

  7. [7]

    Fine, N. J. andSchweigert, G. E.,On the group of homeomorphisms of an arc. Ann. of Math. (2)62 (1955), 237–253.

  8. [8]

    Gottschalk, W. H. andHedlund, G. A.,Topological dynamics. Amer. Math. Soc. Colloq. Publ., Vol. 36, Providence, RI, 1955.

  9. [9]

    Michel, H.,Untersuchungen über stetige, monotone Iterationsgruppen reeller Funktionen ohne Differenzierbarkeitsvoraussetzungen. Publ. Math. Debrecen9 (1952), 13–46.

  10. [10]

    Salzmann, H.,Zahlbereiche I. Vorlesungsausarbeitung, Universität Tübingen.

  11. [11]

    Tabor, J.,On the translation equation occurring in the iteration theory. Demonstratio Math.9 (1976), 119–127.

  12. [12]

    Targonski, G.,Topics in iteration theory. Vandenhoek and Ruprecht, Göttingen, 1981.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Abel, U. A note on the parameters of rational iteration groups. Aeq. Math. 27, 236–241 (1984). https://doi.org/10.1007/BF02192674

Download citation

AMS (1980) subject classification

  • Primary 54H15
  • Secondary 39B10