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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Area and Hausdorff dimension of Julia sets of entire functions


Author: Curt McMullen
Journal: Trans. Amer. Math. Soc. 300 (1987), 329-342
MSC: Primary 30D05; Secondary 58F08, 58F20
MathSciNet review: 871679
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0871679-3
Article copyright: © Copyright 1987 American Mathematical Society