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Landing property of stretching rays for real cubic polynomials


Authors: Yohei Komori and Shizuo Nakane
Journal: Conform. Geom. Dyn. 8 (2004), 87-114
MSC (2000): Primary 37F45; Secondary 37F30
DOI: https://doi.org/10.1090/S1088-4173-04-00102-X
Published electronically: March 29, 2004
MathSciNet review: 2060379
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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: https://doi.org/10.1090/S1088-4173-04-00102-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
Published electronically: March 29, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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