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)

 

Moments of balanced measures on Julia sets


Authors: M. F. Barnsley and A. N. Harrington
Journal: Trans. Amer. Math. Soc. 284 (1984), 271-280
MSC: Primary 30D05; Secondary 30E05, 58F11
MathSciNet review: 742425
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: By a theorem of S. Demko there exists a balanced measure on the Julia set of an arbitrary nonlinear rational transformation on the Riemann sphere. It is proved here that if the transformation admits an attractive or indifferent cycle, then there is a point with respect to which all the moments of a balanced measure exist; moreover, these moments can be calculated exactly. An explicit balanced measure is exhibited in an example where the Julia set is the whole sphere and for which the moments, with respect to any point, do not all exist.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30D05, 30E05, 58F11

Retrieve articles in all journals with MSC: 30D05, 30E05, 58F11


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0742425-6
PII: S 0002-9947(1984)0742425-6
Keywords: Julia sets, orthogonal polynomials
Article copyright: © Copyright 1984 American Mathematical Society