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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Infinite compositions of Möbius transformations

Author: John Gill
Journal: Trans. Amer. Math. Soc. 176 (1973), 479-487
MSC: Primary 30A22; Secondary 40A15
MathSciNet review: 0316690
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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.

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Keywords: Hyperbolic, loxodromic, elliptic Möbius transformations, parabolic Möbius transformations, continued fractions periodic in the limit
Article copyright: © Copyright 1973 American Mathematical Society

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