Multiplier Spectra and the Moduli Space of Degree 3 Morphisms on P1

Details Multiplier Spectra and the Moduli Space of Degree 3 Morphisms on P1 Multiplier Spectra and the Moduli Space of Degree 3 Morphisms on P1

2011-10-23

arxiv.org/abs/1110.5082v1

Mathematics

Number Theory

10 pages

Scientific paper

The moduli space of degree $d$ morphisms on $\mathbb{P}^1$ has received much study. McMullen showed that, except for certain families of Latt\`es maps, there is a finite-to-one correspondence (over $\mathbb{C}$) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms Milnor (over $\mathbb{C}$) and Silverman (over $\mathbb{Z}$) showed that the correspondence is an isomorphism. In this article we address two cases: polynomial maps of any degree and rational maps of degree 3.

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