The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps

Dragos Ghioca, Khoa D. Nguyen, Hexi Ye

We prove the Dynamical Bogomolov Conjecture for endomorphisms of P^1\times P^1 defined over a number field. We use the equidistribution theorem for points of small height with resp…