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

2011/10/23 by Benjamin Hutz, Hutz, Benjamin, Michael Tepper +1 · 3 citations
Mathematics · #37P05 #37P45 #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1110.5082

openalex publication_date 2011/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture
• The McMullen Map in Positive Characteristic
• Periodic curves for general endomorphisms of \mathbb C\mathbb P¹× \mathbb C\mathbb P¹

Related

• Moduli spaces of polynomial maps and multipliers at small cycles
• Multipliers and invariants of endomorphisms of projective space in dimension greater than 1
• The multiplier spectrum morphism is generically injective
• The Space of Morphisms on Projective Space
• Dynamical Systems of Correspondences on the Projective Line II: Degrees of Multiplier Maps