Area and Hausdorff Dimension of Julia Sets of Entire Functions

 
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https://doi.org/10.2307/2000602
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McMullen, Curtis T. 1987. Area and Hausdorff dimension of Julia sets of entire functions. Transactions of the American Mathematical Society 300(1): 329–342.
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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http://nrs.harvard.edu/urn-3:HUL.InstRepos:3597233

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