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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: 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$.

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  • [2] G. Julia, Sur quelques propriétés nouvelles des fonctions entières ou méromorphes (liere Mémoire), Ann. Sci. École Norm. Sup. 36 (1919), 93-125. MR 1509216
  • [3] T. 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 pp. MR 43 #6414. MR 0280695 (43:6414)

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Article copyright: © Copyright 1974 American Mathematical Society

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