Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Conjugacies between rational maps and extremal quasiconformal maps


Author: Guizhen Cui
Journal: Proc. Amer. Math. Soc. 129 (2001), 1949-1953
MSC (2000): Primary 37F30, 30C75
DOI: https://doi.org/10.1090/S0002-9939-01-05918-4
Published electronically: February 22, 2001
MathSciNet review: 1825901
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We show that two rational maps which are $K$-quasiconformally combinatorially equivalent are $K$-quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.


References [Enhancements On Off] (What's this?)

  • [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: https://doi.org/10.1090/S0002-9939-01-05918-4
Keywords: Rational map, extremal quasiconformal map
Received by editor(s): August 21, 1999
Published electronically: February 22, 2001
Additional Notes: This work is supported by the National Natural Sience Foundation of China (No. 19871084)
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society