Uniformly perfect sets, rational semigroups, Kleinian groups and IFS’s
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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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2569-2575
- MSC (1991): Primary 30D05, 58F23
- DOI: https://doi.org/10.1090/S0002-9939-00-05313-2
- MathSciNet review: 1662218