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Completely invariant Julia sets
of polynomial semigroups

Author: Rich Stankewitz
Journal: Proc. Amer. Math. Soc. 127 (1999), 2889-2898
MSC (1991): Primary 30D05, 58F23
Published electronically: April 23, 1999
MathSciNet review: 1600149
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Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. Alan F. Beardon, Iterations of rational functions, Springer-Verlag, New York, 1991. MR 92j:30026
  • 2. A. Hinkkanen and G.J. Martin, The dynamics of semigroups of rational functions I, Proc. London Math. Soc. 73 (1996), 358-384. MR 97e:58198

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Additional Information

Rich Stankewitz

Keywords: Polynomial semigroups, completely invariant sets, Julia sets
Received by editor(s): March 10, 1997
Received by editor(s) in revised form: December 8, 1997
Published electronically: April 23, 1999
Additional Notes: This research was supported by a Department of Education GAANN fellowship and by the Research Board of the University of Illinois at Urbana-Champaign.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1999 American Mathematical Society

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