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Stratification and coordinate systems for the moduli space of rational functions
Author(s):
Masayo
Fujimura;
Masahiko
Taniguchi
Journal:
Conform. Geom. Dyn.
14
(2010),
141-153.
MSC (2010):
Primary 30C15;
Secondary 37F10
Posted:
May 5, 2010
MathSciNet review:
2644836
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Additional information
Abstract:
In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a conjecture of Milnor affirmatively.
References:
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- 2.
- D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry, GTM 185, Springer-Verlag, 1998. MR 1639811 (99h:13033)
- 3.
- M. Fujimura, The moduli space of rational maps and surjectivity of multiplier representation, Comp. Meth. Funct. Th. 7 (2007), 345-360. MR 2376676 (2008k:30049)
- 4.
- M. Fujimura and M. Taniguchi, A compactification of the moduli space of polynomials, Proc. Amer. Math. Soc. 136 (2008), 3601-3609. MR 2415044 (2009d:37081)
- 5.
- C. McMullen, Families of rational maps and iterative root-finding algorithms, Ann. of Math. 125 (1987), 467-493. MR 890160 (88i:58082)
- 6.
- J. Milnor, Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993), 37-83. MR 1246482 (96b:58094)
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- -, Dynamics in one complex variable, third ed., Princeton University Press, 2006. MR 2193309 (2006g:37070)
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Additional Information:
Masayo
Fujimura
Affiliation:
Department of Mathematics, National Defense Academy, Yokosuka 239-8686, Japan
Email:
masayo@nda.ac.jp
Masahiko
Taniguchi
Affiliation:
Department of Mathematics, Nara Women's University, Nara 630-8506, Japan
Email:
tanig@cc.nara-wu.ac.jp
DOI:
10.1090/S1088-4173-10-00207-9
PII:
S 1088-4173(10)00207-9
Received by editor(s):
August 17, 2009
Posted:
May 5, 2010
Additional Notes:
The second author is partially supported by Grant-in-Aid for Scientific Research (C) 19540181.
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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