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

 

On biaccessible points in the Julia set
of a Cremer quadratic polynomial


Authors: Dierk Schleicher and Saeed Zakeri
Journal: Proc. Amer. Math. Soc. 128 (2000), 933-937
MSC (1991): Primary 58F23; Secondary 30D40
Published electronically: July 28, 1999
MathSciNet review: 1637424
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.


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Additional Information

Dierk Schleicher
Affiliation: Fakultät für Mathematik, Technische Universität München, Barer Strasse 23, D-80290 München, Germany
Email: dierk@mathematik.tu-muenchen.de

Saeed Zakeri
Affiliation: Department of Mathematics, SUNY at Stony Brook, New York 11794-3651
Email: zakeri@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05111-4
PII: S 0002-9939(99)05111-4
Keywords: Julia set, Cremer point, biaccessible point, hedgehog
Received by editor(s): February 19, 1998
Received by editor(s) in revised form: May 9, 1998
Published electronically: July 28, 1999
Communicated by: Michael Handel
Article copyright: © Copyright 1999 American Mathematical Society