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Branner-Hubbard-Lavaurs deformations for real cubic polynomials with a parabolic fixed point
Author:
Shizuo Nakane
Journal:
Conform. Geom. Dyn. 13 (2009), 110-123
MSC (2000):
Primary 37F45; Secondary 37F30
Posted:
March 26, 2009
MathSciNet review:
2491720
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Additional Information
Abstract: In this article, we study what we call the Branner-Hubbard-Lavaurs deformation of real cubic polynomials with a parabolic fixed point of multiplier one. It turns out that the existence of non-trivial deformations corresponds to the oscillation of stretching rays and discontinuity of the wring operation.
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P. Willumsen: Holomorphic dynamics: On accumulation of stretching rays. Ph.D. thesis Tech. Univ. Denmark, 1997.
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- B. Branner: Turning around the connectedness locus. In: ``Topological methods in modern Mathematics.'' pp. 391-427. Houston, Publish or Perish, 1993. MR 1215972 (94c:58168)
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- B. Branner and J. Hubbard: The iteration of cubic polynomials. Part I: The global topology of parameter space. Acta Math. 160 (1988), pp. 143-206. MR 945011 (90d:30073)
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- A. Douady: Conjectures about the Branner-Hubbard motion of Cantor sets in
 . In: ``Dynamics on the Riemann sphere.'' pp. 209-222. Euro. Math. Soc., 2006. MR 2348963 (2008j:37103)
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- J. Milnor: Remarks on iterated cubic maps. Experimental Math. 1 (1992), pp. 5-24. MR 1181083 (94c:58096)
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- M. Shishikura: The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets. Annals Math. 147 (1998), pp. 225-267. MR 1626737 (2000f:37056)
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- Tan Lei: Stretching rays and their accumulations, following Pia Willumsen. In: ``Dynamics on the Riemann sphere.'' pp. 183-208. Euro. Math. Soc., 2006. MR 2348962 (2008i:37094)
- [W]
- P. Willumsen: Holomorphic dynamics: On accumulation of stretching rays. Ph.D. thesis Tech. Univ. Denmark, 1997.
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Additional Information
Shizuo Nakane
Affiliation:
Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan
Email:
nakane@gen.t-kougei.ac.jp
DOI:
http://dx.doi.org/10.1090/S1088-4173-09-00192-1
PII:
S 1088-4173(09)00192-1
Keywords:
Branner-Hubbard deformation,
Lavaurs map
Received by editor(s):
July 10, 2008
Posted:
March 26, 2009
Additional Notes:
The author was supported in part by Grant-in-Aid for Scientific Research (No.17540177), Japan Society for the Promotion of Science.
Article copyright:
© Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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