The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P^1)^n

Dragos Ghioca; Hexi Ye; Khoa D. Nguyen

arxiv: 1705.04873 · v1 · pith:M5WN54ZVnew · submitted 2017-05-13 · 🧮 math.NT · math.AG· math.DS

The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P¹)^n

Dragos Ghioca , Khoa D. Nguyen , Hexi Ye This is my paper

classification 🧮 math.NT math.AGmath.DS

keywords dynamicalconjecturebogomolovendomorphismsmanin-mumfordalgebraicanalysiscombined

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We prove Zhang's Dynamical Manin-Mumford Conjecture and Dynamical Bogomolov Conjecture for dominant endomorphisms of (P^1)^n. We use the equidistribution theorem for points of small height with respect to an algebraic dynamical system, combined with an analysis of the symmetries of the Julia set for a rational function.

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The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P¹)^n

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