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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Every direction a Julia direction


Author: Bryan E. Cain
Journal: Proc. Amer. Math. Soc. 46 (1974), 250-252
MSC: Primary 30A66
MathSciNet review: 0349999
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f(z) = \exp (\cosh z)$. If $ N$ is any $ \epsilon $-neighborhood of any ray through the origin with slope $ m \ne 0,\infty $ then $ {f^{ - 1}}(w) \cap N$ is infinite if $ w \ne 0$.


References [Enhancements On Off] (What's this?)

  • [1] Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Co., Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608 (34 #1490)
  • [2] Gaston Julia, Sur quelques propriétés nouvelles des fonctions entières ou méromorphes (premier mémoire), Ann. Sci. École Norm. Sup. (3) 36 (1919), 93–125 (French). MR 1509216
  • [3] Toshiko Zinno, Some properties of Julia’s exceptional functions and an example of Julia’s exceptional functions with Julia’s direction, Ann. Acad. Sci. Fenn. Ser. A I No. 464 (1970), 12. MR 0280695 (43 #6414)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0349999-7
PII: S 0002-9939(1974)0349999-7
Article copyright: © Copyright 1974 American Mathematical Society