Area and Hausdorff dimension of Julia sets of entire functions
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- by Curt McMullen
- Trans. Amer. Math. Soc. 300 (1987), 329-342
- DOI: https://doi.org/10.1090/S0002-9947-1987-0871679-3
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Abstract:
We show the Julia set of $\lambda \sin (z)$ has positive area and the action of $\lambda \sin (z)$ on its Julia set is not ergodic; the Julia set of $\lambda \exp (z)$ has Hausdorff dimension two but in the presence of an attracting periodic cycle its area is zero.References
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Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 300 (1987), 329-342
- MSC: Primary 30D05; Secondary 58F08, 58F20
- DOI: https://doi.org/10.1090/S0002-9947-1987-0871679-3
- MathSciNet review: 871679