Interesting Esoterica

Area and Hausdorff Dimension of Julia Sets of Entire Functions

by Curt McMullen
  • Published in 1987
  • Added on
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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BibTeX entry

@misc{item58,
	title = {Area and Hausdorff Dimension of Julia Sets of Entire Functions},
	author = {Curt McMullen},
	url = {http://www.math.harvard.edu/{\~{}}ctm/papers/home/text/papers/entire/entire.pdf},
	urldate = {2015-12-17},
	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.},
	comment = {},
	year = 1987
}