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Compositions of linear-fractional transformations
V. I. Buslaeva, S. F. Buslaevab a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Mathematics, Ukrainian National Academy of Sciences
Abstract:
We study the asymptotic behavior of the compositions (Sn∘⋯∘S1)(z) and (S1∘⋯∘Sn)(z) of linear-fractional transformations Sn(z) (n=1,2,…) whose fixed points have limits. In particular, if Sn(z)=αn(βn+z)−1, then the sequence of compositions (S1∘⋯∘Sn)(z) at the point z=0 coincides with the sequence of convergents of the formal continued fraction
α1β1+α2β2+⋯.
The result obtained can be applied in the study of convergence of formal continued fractions.
Received: 10.11.1996
Citation:
V. I. Buslaev, S. F. Buslaeva, “Compositions of linear-fractional transformations”, Mat. Zametki, 61:3 (1997), 332–338; Math. Notes, 61:3 (1997), 272–277
Linking options:
https://www.mathnet.ru/eng/mzm1507https://doi.org/10.4213/mzm1507 https://www.mathnet.ru/eng/mzm/v61/i3/p332
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Abstract page: | 403 | Full-text PDF : | 235 | References: | 93 | First page: | 1 |
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