CONTINUED FRACTIONS AND RESTRAINED SEQUENCES OF MÖBIUS MAPS

CONTINUED FRACTIONS AND RESTRAINED SEQUENCES OF MÖBIUS MAPS

Modified approximants of a continued fraction are designed to increase the rate of convergence, and these led to the notion of restrained sequences of Möbius transformations. Here we give some analytic and geometric characterizations of restrained sequences and related topics. We also give an exposi...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2004-06, Vol.34 (2), p.441-466
Hauptverfasser: BEARDON, A.F., LORENTZEN, L.
Format: Artikel
Sprache:eng
Schlagworte:
Circles
Continued fractions
Geometry
Hyperbolic geometry
Mathematical sequences
Mathematical theorems
Perceptron convergence procedure
Radius of a sphere
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Zusammenfassung:Modified approximants of a continued fraction are designed to increase the rate of convergence, and these led to the notion of restrained sequences of Möbius transformations. Here we give some analytic and geometric characterizations of restrained sequences and related topics. We also give an expository account of the use of geometry, including hyperbolic geometry, in discussing restrained sequences and continued fractions.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1181069862