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Uniformly perfect sets, rational semigroups, Kleinian groups and IFS's |
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| Authors: | Rich Stankewitz |
| Institution: | Department of Mathematics, Texas A&M University, College Station, Texas 77843 |
| Abstract: | We show that the Julia set of a non-elementary rational semigroup |
| Keywords: | Rational semigroups Kleinian groups Julia sets uniformly perfect iterated function systems |
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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.