Landing property of stretching rays for real cubic polynomials
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- by Yohei Komori and Shizuo Nakane
- Conform. Geom. Dyn. 8 (2004), 87-114
- DOI: https://doi.org/10.1090/S1088-4173-04-00102-X
- Published electronically: 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.References
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Bibliographic 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
- MR Author ID: 190353
- Email: nakane@gen.t-kougei.ac.jp
- Received by editor(s): May 15, 2003
- Received by editor(s) in revised form: November 20, 2003
- Published electronically: March 29, 2004
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2060379