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

Abstract

The moduli space of degree $d$ morphisms on ${\mathbb{P}}^1$ has received much study. McMullen showed that, except for certain families of Lattès 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.

This version includes the code for the computations (which are not in the journal publication). To appear in JP Journal of Algebra, Number Theory and Applications

References in corpus (1)

• The Space of Morphisms on Projective Space

Cited by in corpus (4)

• Attracting cycles in p-adic dynamics and height bounds for post-critically finite maps
• An Algebraic Proof of Thurston's Rigidity for a Polynomial
• Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line
• The McMullen Map in Positive Characteristic