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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Every direction a Julia direction
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by Bryan E. Cain PDF
Proc. Amer. Math. Soc. 46 (1974), 250-252 Request permission

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
  • Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
  • 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
  • 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
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 46 (1974), 250-252
  • MSC: Primary 30A66
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0349999-7
  • MathSciNet review: 0349999