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On biaccessible points in the Julia set of a Cremer quadratic polynomial
Author(s):
Dierk
Schleicher;
Saeed
Zakeri
Journal:
Proc. Amer. Math. Soc.
128
(2000),
933-937.
MSC (1991):
Primary 58F23;
Secondary 30D40
Posted:
July 28, 1999
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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:
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
Posted:
July 28, 1999
Communicated by:
Michael Handel
Copyright of article:
Copyright
1999,
American Mathematical Society
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