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arXiv · 1705.04873

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

Dragos Ghioca·Khoa D. Nguyen·Hexi Ye
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Abstract

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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Dragos Ghioca, Khoa D. Nguyen, Hexi Ye. 2017-05-13. The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for endomorphisms of (P^1)^n. https://doi.org/10.1112/s0010437x18007157

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