2013/12/05 by Rich Stankewitz, Stankewitz, Rich, Hiroki Sumi +1
Mathematics · #30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Probability (math.PR) #math.CV #math.DS #math.GT #math.PR #msc:30D05 #msc:37F10
paper · pdf · doi:10.48550/arxiv.1312.1457
15 pages
arxiv created 2013/12/05 · arxiv updated 2013/12/06
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 pictures of the Julia sets, previously proven to work in the context of iteration of a rational map of degree two or more, extends to finitely generated rational semigroups (of a certain type). We also provide some consequences of this result.