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Completely invariant Julia sets of polynomial semigroups
Author(s):
Rich
Stankewitz
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2889-2898.
MSC (1991):
Primary 30D05, 58F23
Posted:
April 23, 1999
MathSciNet review:
1600149
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Abstract:
Let  be a semigroup of rational functions of degree at least two, under composition of functions. Suppose that  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  , is the sphere itself.
References:
- 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
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Address at time of publication:
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email:
rich.stankewitz@math.tamu.edu
DOI:
10.1090/S0002-9939-99-04857-1
PII:
S 0002-9939(99)04857-1
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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