Every direction a Julia direction
HTML articles powered by AMS MathViewer
- 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
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