Area and Hausdorff Dimension of Julia Sets of Entire Functions

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Area and Hausdorff Dimension of Julia Sets of Entire Functions

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Title: Area and Hausdorff Dimension of Julia Sets of Entire Functions
Author: McMullen, Curtis T.
Citation: McMullen, Curtis T. 1987. Area and Hausdorff dimension of Julia sets of entire functions. Transactions of the American Mathematical Society 300(1): 329–342.
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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.
Published Version: doi:10.2307/2000602
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3597233

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  • FAS Scholarly Articles [6466]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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