# Area and Hausdorff Dimension of Julia Sets of Entire Functions

• Published in 1987
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.

### 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
}