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Completely invariant Julia sets of polynomial semigroups

1998/10/14 by Rich Stankewitz, Stankewitz, Rich
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/9810090

10 pages

arxiv created 1998/10/14 · arxiv updated 2009/11/30

Abstract

Let G be a semigroup of rational functions of degree at least two, under composition of functions. Suppose that G contains two polynomials with non-equal Julia sets. We prove that the smallest closed subset of the Riemann sphere which contains at least three points and is completely invariant under each element of G, is the sphere itself.

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