Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T23:58:19.915Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Barth, K., Asymptotic values of meromorphic functions, Mich. Math. J., 13 (1966), 321–340.Google Scholar
[2] Collingwood, E. F., A boundary theorem for Tsuji functions, Nagoya Math. J., 29 (1967), 197–200.Google Scholar
[3] Collingwood, E. F. and Piranian, G., Tsuji functions with segments of Julia, Math. Z., 84 (1964), 246–253.Google Scholar
[4] Gauthier, P., A criterion for normalcy, Nagoya Math. J., 32 (1968), 277–282.CrossRefGoogle Scholar
[5] Hayman, W. K., The boundary behavior of Tsuji functions, Mich. Math. J., 15 (1968), 1–26.CrossRefGoogle Scholar
[6] Lappan, P., Some sequential properties of normal and non-normal functions with applications to automorphic functions, Comm. Math. Univ. Sancti Pauli, 12 (1964), 41–57.Google Scholar
[7] Tse, K.-F., Some results on value distribution of meromorphic functions in the unit disk, Nagoya Math. J., 34 (1969), 105–119.Google Scholar