1998/10/14 by Rich Stankewitz, Stankewitz, Rich · 1 citation
Mathematics · #30D05 #58F23 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:30D05 #msc:58F23
paper · pdf · doi:10.48550/arxiv.math/9810089
6 pages
arxiv created 1998/10/14 · arxiv updated 2009/11/30
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 Moebius 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.