Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Completely invariant Julia sets
of polynomial semigroups

Author: Rich Stankewitz
Journal: Proc. Amer. Math. Soc. 127 (1999), 2889-2898
MSC (1991): Primary 30D05, 58F23
Published electronically: April 23, 1999
MathSciNet review: 1600149
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $G$ be a semigroup of rational functions of degree at least two, under composition of functions. Suppose that $G$ contains two polynomials with non-equal Julia sets. We prove that the smallest closed subset of the Riemann sphere which contains at least three points and is completely invariant under each element of $G$, is the sphere itself.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D05, 58F23

Retrieve articles in all journals with MSC (1991): 30D05, 58F23

Additional Information

Rich Stankewitz

PII: S 0002-9939(99)04857-1
Keywords: Polynomial semigroups, completely invariant sets, Julia sets
Received by editor(s): March 10, 1997
Received by editor(s) in revised form: December 8, 1997
Published electronically: April 23, 1999
Additional Notes: This research was supported by a Department of Education GAANN fellowship and by the Research Board of the University of Illinois at Urbana-Champaign.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia