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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Translation invariant Julia sets


Author: David Boyd
Journal: Proc. Amer. Math. Soc. 128 (2000), 803-812
MSC (1991): Primary 30D05
Published electronically: July 6, 1999
MathSciNet review: 1625697
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Abstract: We show that if the Julia set $J(f)$ of a rational function $f$ is invariant under translation by one and infinity is a periodic or preperiodic point for $f$, then $J(f)$ must either be a line or the Riemann sphere.


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Additional Information

David Boyd
Email: boyd@math.uiuc.edu, boyd@math.purdue.edu

DOI: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 1999 American Mathematical Society