Skip Navigation

Journal of the London Mathematical Society 2002 65(2):453-463; doi:10.1112/S0024610701003027
© 2002 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Inninger, C.
Right arrow Articles by Peherstorfer, F.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

A New Simple Class of Rational Functions whose Julia Set is the whole Riemann Sphere

Clemens Inninger and Franz Peherstorfer

Institut für Analysis, Universität Linz Altenbergerstrasse 69, 4040 Linz, Austria, clemensinninger{at}hotmail.com
Institut für Analysis, Universität Linz Altenbergerstrasse 69, 4040 Linz, Austria, franz.peherstorfer{at}jk.uni-linz.ac.at

Received 9 August 2000. Revision received 26 June 2001.

The paper first gives sufficient conditions on the critical points and the Schwarzian derivative of a real rational function R such that the Julia set of R is Formula. Further, it is shown that under mild conditions on another real rational function Formula with possibly non-empty Fatou set, the Julia set of Formula {circ} R is the whole Riemann sphere again. Then families of rational functions are given whose Julia set is Formula and whose critical points are not necessarily preperiodic. Concrete examples were previously available only for the preperiodic case. Finally, it is demonstrated that the methods presented also apply to the construction of polynomials whose Julia sets are dendrites and whose critical points in the Julia set are not necessarily preperiodic.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.