|
Branner-Hubbard-Lavaurs deformations for real cubic polynomials with a parabolic fixed point
Author(s):
Shizuo
Nakane
Journal:
Conform. Geom. Dyn.
13
(2009),
110-123.
MSC (2000):
Primary 37F45;
Secondary 37F30
Posted:
March 26, 2009
MathSciNet review:
2491720
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
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.
References:
-
- [B]
- 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)
- [BH]
- 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)
- [D]
- 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) - [KN]
- Y. Komori and S. Nakane: Landing property of stretching rays for real cubic polynomials. Conformal Geometry and Dynamics 8 (2004), pp. 87-114. MR 2060379 (2005d:37092)
- [M]
- J. Milnor: Remarks on iterated cubic maps. Experimental Math. 1 (1992), pp. 5-24. MR 1181083 (94c:58096)
- [PT]
- C. L. Petersen and Tan Lei: Branner-Hubbard motions and attracting dynamics. In: ``Dynamics on the Riemann sphere.'' pp. 45-70. Euro. Math. Soc., 2006. MR 2348954 (2008j:37092)
- [S]
- 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)
- [T]
- 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.
Similar Articles:
Retrieve articles in Conformal Geometry and Dynamics
with MSC
(2000):
37F45,
37F30
Retrieve articles in all Journals with MSC
(2000):
37F45,
37F30
Additional Information:
Shizuo
Nakane
Affiliation:
Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan
Email:
nakane@gen.t-kougei.ac.jp
DOI:
10.1090/S1088-4173-09-00192-1
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.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
