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On dynamical Teichmüller spaces
Author(s):
Carlos
Cabrera;
Peter
Makienko
Journal:
Conform. Geom. Dyn.
14
(2010),
256-268.
MSC (2010):
Primary 37F30, 37F10;
Secondary 37F50
Posted:
October 13, 2010
MathSciNet review:
2729366
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Abstract:
Following ideas from a preprint of the second author (see Automorphisms of a rational function with disconnected Julia set, Orsay, Preprint, 03 1992), we investigate relations of dynamical Teichmüller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and laminations in holomorphic dynamics (see J. Diff. Geom. 47 (1997), 17-94).
References:
-
- 1.
- X. Buff and A. L. Epstein, From local to global analytic conjugacies, Ergod. Th. & Dynam. Sys. 27 (2007), no. 4, 1073-1094. MR 2342966 (2008g:37039)
- 2.
- M. Lyubich and Y. Minsky, Laminations in holomorphic dynamics, J. Diff. Geom. 47 (1997), 17-94. MR 1601430 (98k:58191)
- 3.
- P. Makienko, Automorphisms of a rational function with disconnected Julia set, Orsay, Preprint, 03 1992.
- 4.
- R. Mañé, P. Sad, and D. Sullivan, On the dynamics of rational maps, Ann. Scien. Ec. Norm. Sup., Paris(4) (1983).
- 5.
- C. McMullen, Automorphisms of rational functions, Holomorphic functions and moduli I. (D. Drasin et al., eds.), Springer-Verlag, 1986, pp. 31-60. MR 955807 (89m:58187)
- 6.
- C. McMullen and D. Sullivan, Quasiconformal homeomorphisms and dynamics III: The Teichmüller space of a holomorphic dynamical system, 1998.
- 7.
- D. Sullivan, Seminar on conformal and hyperbolic geometry by D. P. Sullivan (Notes by M. Baker and J. Seade), Preprint IHES, 1982.
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Additional Information:
Carlos
Cabrera
Affiliation:
Instituto de Matematicas UNAM, Av Universidad S/N Col Lomas de Chamilpa Cuernavaca, 62100 Cuernavaca MO, Mexico
Email:
carlos@matcuer.unam.mx
Peter
Makienko
Affiliation:
University Nacional Autonoma de Mexico, Institute of Mathematics, Av Universidad s/n, O P 62210 Morelos, Mexico
Email:
makienko@matcuer.unam.mx
DOI:
10.1090/S1088-4173-2010-00214-6
PII:
S 1088-4173(2010)00214-6
Keywords:
Holomorphic dynamics,
Teichmüller theory.
Received by editor(s):
November 30, 2009
Posted:
October 13, 2010
Additional Notes:
This work was partially supported by PAPIIT project IN 100409.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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