12 citations · 19 across the 10 of their papers we have counts for
10 papers
Hereditarily non Uniformly Perfect non-Autonomous Julia Sets
Mark Comerford, Rich Stankewitz, Hiroki Sumi
Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in \cite{SSS} who gave several examples of such sets based on Cantor set-like constru…
Hereditarily Non Uniformly Perfect Sets
Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi
We introduce the concept of hereditarily non uniformly perfect sets, compact sets for which no compact subset is uniformly perfect, and compare them with the following: Hausdorff d…
Backward Iteration Algorithms for Julia sets of Möbius Semigroups
Rich Stankewitz, Hiroki Sumi
We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-Möbius element) to a cla…
Random Backward Iteration Algorithm for Julia sets of Rational Semigroups
Rich Stankewitz, Hiroki Sumi
We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the picture…
Some counterexamples in dynamics of rational semigroups
Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi
We give an example of two rational functions with non-equal Julia sets that generate a rational semigroup whose completely invariant Julia set is a closed line segment. We also giv…
Uniformly perfect analytic and conformal attractor sets
Rich Stankewitz
Conditions are given which imply that analytic iterated function systems (IFS's) in the complex plane have uniformly perfect attractor sets. In particular, it is shown that the att…