Rocky Mountain Journal of Mathematics

Iteration of Möbius transforms and continued fractions

Johan Karlsson, Hans Wallin, and Jan Gelfgren

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 21, Number 1 (1991), 451-472.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181073017

Digital Object Identifier
doi:10.1216/rmjm/1181073017

Mathematical Reviews number (MathSciNet)
MR1113937

Zentralblatt MATH identifier
0734.30006

Citation

Karlsson, Johan; Wallin, Hans; Gelfgren, Jan. Iteration of Möbius transforms and continued fractions. Rocky Mountain J. Math. 21 (1991), no. 1, 451--472. doi:10.1216/rmjm/1181073017. https://projecteuclid.org/euclid.rmjm/1181073017


Export citation

References

  • C. Baltus and W.B. Jones, Truncation error bounds for modified continued fractions with applications to special functions, to appear in Numer. Math.
  • P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. 11 (1984), 85-141.
  • J.D. de Pree and W.J. Thron, On sequences of Moebius transformations, Math. Z. 80 (1962), 184-93.
  • L.R. Ford, Automorphic functions, 2nd ed. Chelsea, New York, 1929.
  • J. Gill, Infinite compositions of Möbius transformations, Trans. Amer. Math. Soc. 176 (1973), 479-87.
  • --------, Convergence acceleration for continued fractions $K(a_n/1)$\noindent with $\lim a_n=0$, Lecture Notes in Mathematics, vol. 932, Springer, New York, 1982, 67-70.
  • --------, Limit periodic iteration, to appear in J. Appl. Numer. Math.
  • --------, Composition of analytic functions of the form $F_n(z)=F_n-1(f_n(z))$, $f_n(z)\to f(z)$, to appear in J. Comput. Appl. Math.
  • P. Henrici, Applied and computational complex analysis, Vol. 2, John Wiley and Sons, New York, 1977.
  • L. Jacobsen, Convergence acceleration and analytic continuation by means of modifications of continued fractions, Det Kongl. Norske Videnskabers Selskab Skrifter no. 1, 1983, 19 -33.
  • --------, On the Convergence of limit periodic continued fractions $K(a_n/1)$, where $a_n\to-1/4$. Part II, Lecture Notes in Mathematics, vol. 1199, Springer, New York, (1986), 48-58.
  • --------, Convergence of limit $k$-periodic continued fractions $K(a_n/b_n)$ and of subsequences of their tails, Proc. London Math. Soc. (3) 51 (1985), 563-76.
  • --------, Composition of linear fractional transformations in terms of tail sequences, Proc. Amer. Math. Soc. 97 (1986), 97-104.
  • --------, General convergence of continued fractions, Trans. Amer. Math. Soc. 294 (1986), 477-85.
  • --------, Convergence of limit $k$-periodic continued fractions in the hyperbolic or loxodromic case, Det Kongl. Norske Videnskabers Selskab Skrifter no. 5, 1987.
  • L. Jacobsen and A. Magnus, On the convergence of limit periodic continued fractions $K(a_n/1)$ where $a_n\to-1/4$, Lecture Notes in Mathematics, vol. 1105, Springer, New York, 1984, 243-48.
  • L. Jacobsen and W.J. Thron, Limiting structures for sequences of linear fractional transformations, Proc. Amer. Math. Soc. 99 (1987), 141-46.
  • L. Jacobsen and H. Waadeland, An asymptotic property for tails of limit periodic continued fractions, to appear.
  • W.B. Jones and W.J. Thron, Continued fractions: analytic theory and applications, Encycl. of Math. Appl., vol. 11, Addison-Wesley, Reading, MA, 1980.
  • N.J. Kalton and L.J. Lange, Equimodular limit periodic continued fractions, Lecture Notes in Mathematics, vol. 1199, Springer, New York, 1986, 159-219.
  • M. Mandell and A. Magnus, On convergence of sequences of linear fractional transformations, Math. Z. 115 (1970), 11-17.
  • G. Piranian and W.J. Thron, Convergence properties of sequences of linear fractional transformations, Michigan Math. J. 4 (1957), 129-35.
  • W.J. Thron, Another look at the definition of strong convergence of continued fractions, Det Kongl. Norske Videnskabers Selskab Skrifter no. 1, 1983, 128-35.
  • W.J. Thron and H. Waadeland, Accelerating convergence of limit periodic continued fractions $K(a_n/1)$, Numer. Math. 34 (1980), 155-70.