The multiplier spectrum morphism is generically injective

Autor:	Ji, Zhuchao, Xie, Junyi
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexible Latt\`es family, the multiplier spectrum morphism is quasi-finite. In this paper, we strengthen McMullen's theorem by showing that the multiplier spectrum morphism is generically injective. This answers a question of McMullen and Poonen. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.15382 Zobrazit plný text záznamu View this record from Arxiv