Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D05

Retrieve articles in all journals with MSC (1991): 30D05

Additional Information

David Boyd

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

American Mathematical Society