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

الأصل · EN

The moduli space of degree d morphisms on P¹ has received much study. McMullen showed that, except for certain families of Lattès maps, there is a finite-to-one correspondence (over C) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms Milnor (over C) and Silverman (over 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.