Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

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

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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