Infinite compositions of Möbius transformations
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- by John Gill PDF
- Trans. Amer. Math. Soc. 176 (1973), 479-487 Request permission
Abstract:
A sequence of Möbius transformations $\{ {t_n}\} _{n = 1}^\infty$, which converges to a parabolic or elliptic transformation t, may be employed to generate a second sequence $\{ {T_n}\} _{n = 1}^\infty$ by setting ${T_n} = {t_1} \circ \cdots \circ {t_n}$. The convergence behavior of $\{ {T_n}\}$ is investigated and the ensuing results are shown to apply to continued fractions which are periodic in the limit.References
- Michael Mandell and Arne Magnus, On convergence of sequences of linear fractional transformations, Math. Z. 115 (1970), 11–17. MR 258976, DOI 10.1007/BF01109744 L. R. Ford, Automorphic functions, McGraw-Hill, New York, 1929. T. J. I’A.Bromwich, An introduction to the theory of infinite series, Macmillan, London, 1947.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 176 (1973), 479-487
- MSC: Primary 30A22; Secondary 40A15
- DOI: https://doi.org/10.1090/S0002-9947-1973-0316690-6
- MathSciNet review: 0316690