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

Stankewitz, Rich

doi:10.1090/S0002-9939-00-05313-2

Uniformly perfect sets, rational semigroups, Kleinian groups and IFS’s
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Proc. Amer. Math. Soc. 128 (2000), 2569-2575 Request permission

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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