Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Area and Hausdorff dimension of Julia sets of entire functions


Author: Curt McMullen
Journal: Trans. Amer. Math. Soc. 300 (1987), 329-342
MSC: Primary 30D05; Secondary 58F08, 58F20
MathSciNet review: 871679
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30D05, 58F08, 58F20

Retrieve articles in all journals with MSC: 30D05, 58F08, 58F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0871679-3
PII: S 0002-9947(1987)0871679-3
Article copyright: © Copyright 1987 American Mathematical Society