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

DOI:
https://doi.org/10.1090/S0002-9939-00-05313-2

Published electronically:
February 29, 2000

MathSciNet review:
1662218

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We show that the Julia set of a non-elementary rational semigroup is uniformly perfect when there is a uniform bound on the Lipschitz constants of the generators of . 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:
https://doi.org/10.1090/S0002-9939-00-05313-2

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