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Meromorphic Functions with Large Sets of Julia Points

Published online by Cambridge University Press:  22 January 2016

Peter Colwell
Peter Colwell*
Affiliation:
Department of Mathematics, Iowa State University
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Let D = {z : |z| < 1} and C = {z : |z| = 1}. If W denotes the Riemann sphere equipped the chordal metric X, let f: D → W be meromorphic. A chord T lying in D except for an endpoint γ ∈ C is called a Julia segment for f if for each Stolz angle Δ in D at γ which contains T, f assumes infinitely often in Δ all values of W with at most two exceptions. We call γ ∈ C a Julia point for f if every chord in D ending at γ is a Julia segment for f, and we denote by J(f) the set of Julia points of f.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 50 , June 1973 , pp. 1 - 6
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

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