Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T16:38:17.321Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Values Along Julia Rays

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier and
J. S. Hwang
P. M. Gauthier
Affiliation:
Université de Montréal, Montréal, Québec
J. S. Hwang
Affiliation:
McMaster University, Hamilton, Ontario
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 ƒ be a function meromorphic in the finite complex plane C. If for some number θ, 0 ≦ θ < 2 π, the family, fr(z) = f(reθz), is not normal at z = 1, then the ray arg z = θ is called a Julia ray. Such a ray has the property that in every sector containing it, F assumes every value infinitely often with at most two exceptions. Many authors have taken this property as the definition of a Julia ray.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976, pp. 1210 - 1215
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Arakelian, N. U., Uniform and asymptotic approximation by entire functions on unbounded closed sets, (Russian) Dokl. Akad. Nauk SSSR 157 (1964), 9–11.Google Scholar
2. Bagemihl, F., Erdôs, P., et Seidel, W., Sur quelques propriétés frontières des fonctions holomorphes définies par certains produits dans le cercle-unité. Ann. Sci. Ecole Norm. Sup. (3) 70 (1953), 135–147.Google Scholar
3. Baker, I. N., and Liverp∞l, L. S. O., Further results on Picard sets of entire functions, Proc. London Math. Soc. (3) 26 (1973), 82–98.Google Scholar
4. Barth, K. F., and Schneider, W. J., On a problem of C. Rényi concerning Julia lines, J. Approximation Theory 6 (1972), 312–315.Google Scholar
5. Brown, Leon, Gauthier, P. M., and Seidel, W., Possibility of complex asymptotic approximation on closed sets. Math. Ann. 218 (1975), 1–8.Google Scholar
6. Carleman, T., Sur un théorème de Weierstrass, Ark. Mat. Astronom. Fys. 20B (1927), 1–5.Google Scholar
7. Gauthier, P. M., Cercles de remplissage and asymptotic behaviour along circuitous paths, Can. J. Math. 22 (1970), 389–393.Google Scholar
8. Gross, W., TJber die Singularitaten analytischer Funktionen, Monatsh. Math. 29 (1918), 3–47.Google Scholar
9. Hayman, W. K., Research problems in function theory (Athlone Press, London, 1967).Google Scholar
10. Noshiro, K., Cluster sets (Springer-Verlag, Berlin, 1960).Google Scholar
11. Roth, A., Approximationseigenschaften und Strahlengrenzwerte meromorpher und ganzer Funktionen, Comment. Math. Helv. 11 (1938), 77–125.Google Scholar