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

 

Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's


Author: Rich Stankewitz
Journal: Proc. Amer. Math. Soc. 128 (2000), 2569-2575
MSC (1991): Primary 30D05, 58F23
Published electronically: February 29, 2000
MathSciNet review: 1662218
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Abstract:

We show that the Julia set of a non-elementary rational semigroup $G$is uniformly perfect when there is a uniform bound on the Lipschitz constants of the generators of $G$. This also proves that the limit set of a non-elementary Möbius group is uniformly perfect when there is a uniform bound on the Lipschitz constants of the generators of the group and this implies that the limit set of a finitely generated non-elementary Kleinian group is uniformly perfect.


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Additional Information

Rich Stankewitz
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: richs@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05313-2
PII: S 0002-9939(00)05313-2
Keywords: Rational semigroups, Kleinian groups, Julia sets, uniformly perfect, iterated function systems
Received by editor(s): August 26, 1998
Received by editor(s) in revised form: October 5, 1998
Published electronically: February 29, 2000
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society