Computational Methods and Function Theory 7 (2007), No. 2, 345--360
Copyright Heldermann Verlag 2007
Masayo Fujimura
masayo@nda.ac.jp , National Defense Academy, Department of Mathematics, Yokosuka, 239-8686, Japan.
In this paper, we first show that the map ΨRatn of the moduli space of rational maps of degree n to Cn obtained from multipliers at fixed points is always surjective, while the map ΨPolyn of the moduli space of polynomials of degree n to Cn-1 defined similarly is never so if n≥ 4. Next, in the latter case, we give a sufficient condition and a necessary one for points not in the image of ΨPolyn consists of and give an explicit parametrization for all such points if n=4 or 5. Also, we show that the preimage of a generic point by ΨPolyn consists of (n-2)! points.
Keywords: Rational maps, fixed points, multiplier, moduli space.
MSC 2000: Primary 30C10; Secondary 37C25.
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