Area and Hausdorff Dimension of Julia Sets of Entire Functions

• Published in 1987
• Added on 2015-12-17

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.

Links

• http://www.math.harvard.edu/~ctm/papers/home/text/papers/entire/entire.pdf

Other information

BibTeX entry

@misc{item58,
	key = {item58},
	type = {misc},
	title = {Area and Hausdorff Dimension of Julia Sets of Entire Functions},
	author = {Curt McMullen},
	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 = {},
	date_added = {2015-12-17},
	date_published = {1987-12-07},
	urls = {http://www.math.harvard.edu/{\~{}}ctm/papers/home/text/papers/entire/entire.pdf},
	collections = {},
	url = {http://www.math.harvard.edu/{\~{}}ctm/papers/home/text/papers/entire/entire.pdf},
	urldate = {2015-12-17},
	year = 1987
}