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Translation invariant Julia sets
Author(s):
David
Boyd
Journal:
Proc. Amer. Math. Soc.
128
(2000),
803-812.
MSC (1991):
Primary 30D05
Posted:
July 6, 1999
MathSciNet review:
1625697
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Abstract:
We show that if the Julia set  of a rational function  is invariant under translation by one and infinity is a periodic or preperiodic point for  , then  must either be a line or the Riemann sphere.
References:
- 1.
- I.N. Baker and A. Eremenko. A problem on Julia sets. Ann. Acad. Sci. Fenn., 12:229-236, 1987. MR 89g:30047
- 2.
- Alan F. Beardon. Symmetries of Julia sets. Bull. London Math. Soc., 22:576-582, 1990. MR 92f:30033
- 3.
- Alan F. Beardon. Iterations of Rational Functions. Springer-Verlag, New York, 1991. MR 92j:30026
- 4.
- G. Levin and F. Przytycki. When do two rational functions have the same Julia set? Proc. Amer. Math. Soc., 125(7):2179-2190, 1997. MR 97i:58149
- 5.
- G.M. Levin. Symmetries on the Julia set. Math. Notes, 48.5-6:1126-1131, 1991. MR 92e:30015
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Additional Information:
David
Boyd
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Address at time of publication:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
boyd@math.uiuc.edu, boyd@math.purdue.edu
DOI:
10.1090/S0002-9939-99-05042-X
PII:
S 0002-9939(99)05042-X
Received by editor(s):
November 10, 1997
Received by editor(s) in revised form:
April 27, 1998
Posted:
July 6, 1999
Additional Notes:
Research 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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