|
Conjugacies between rational maps and extremal quasiconformal maps
Author(s):
Guizhen
Cui
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1949-1953.
MSC (2000):
Primary 37F30, 30C75
Posted:
February 22, 2001
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that two rational maps which are  -quasiconformally combinatorially equivalent are  -quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.
References:
-
- [EM]
- C. Earle and C. McMullen, Quasiconformal isotopies, In Holomorphic Functions and Moduli I, Springer-Verlag, MSRI publications 10 (1988), 143-154. MR 89h:30028
- [DH1]
- A. Douady and J. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. Éc. Norm. Sup. 18 (1985), 287-344. MR 87f:58083
- [DH2]
- A. Douady and J. Hubbard, A proof of Thurston's topological characterization of rational maps, Acta Math. 171 (1993), 263-297. MR 94j:58143
- [Mc1]
- C. McMullen, Complex dynamics and Renormalization, Annals of Math Studies 135, Princeton University Press, 1994. MR 96b:58097
- [Mc2]
- -, Automorphisms of rational maps, In Holomorphic Functions and Moduli I, Springer-Verlag, MSRI publications 10 (1988), 31-60. MR 89m:58187
- [Mc3]
- -, Self-similarity of Siegel disks and Hausdorff dimension of Julia sets, Acta Math. 180 (1998), 247-292. MR 99f:58172
- [Oh]
- H. Ohtake, Lifts of extremal quasiconformal mappings of arbitrary Riemann surfaces, J. Math. Kyoto Univ. 22 (1982), 191-200. MR 84e:30071
- [Ri]
- S. Rickman, Removability theorems for quasiconformal mappings, Ann. Ac. Scient. Fenn. 449 (1969), 1-8. MR 40:7443
- [S]
- K. Strebel, On quasiconformal mappings of open Riemann surfaces, Comm. Math. Helv. 53 (1978), 301-321. MR 81i:30041
- [Su]
- D. Sullivan, Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. 122 (1985), 401-418. MR 87i:58103
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
37F30, 30C75
Retrieve articles in all Journals with MSC
(2000):
37F30, 30C75
Additional Information:
Guizhen
Cui
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
Email:
gzcui@math08.math.ac.cn
DOI:
10.1090/S0002-9939-01-05918-4
PII:
S 0002-9939(01)05918-4
Keywords:
Rational map,
extremal quasiconformal map
Received by editor(s):
August 21, 1999
Posted:
February 22, 2001
Additional Notes:
This work is supported by the National Natural Sience Foundation of China (No. 19871084)
Communicated by:
Michael Handel
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org