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Landing property of stretching rays for real cubic polynomials
Author(s):
Yohei
Komori;
Shizuo
Nakane
Journal:
Conform. Geom. Dyn.
8
(2004),
87-114.
MSC (2000):
Primary 37F45;
Secondary 37F30
Posted:
March 29, 2004
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Abstract:
The landing property of the stretching rays in the parameter space of bimodal real cubic polynomials is completely determined. Define the Böttcher vector by the difference of escaping two critical points in the logarithmic Böttcher coordinate. It is a stretching invariant in the real shift locus. We show that stretching rays with non-integral Böttcher vectors have non-trivial accumulation sets on the locus where a parabolic fixed point with multiplier one exists.
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Additional Information:
Yohei
Komori
Affiliation:
Department of Mathematics, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan
Email:
komori@sci.osaka-cu.ac.jp
Shizuo
Nakane
Affiliation:
Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan
Email:
nakane@gen.t-kougei.ac.jp
DOI:
10.1090/S1088-4173-04-00102-X
PII:
S 1088-4173(04)00102-X
Keywords:
Stretching rays,
parabolic implosion,
radial Julia set
Received by editor(s):
May 15, 2003
Received by editor(s) in revised form:
November 20, 2003
Posted:
March 29, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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