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arXiv · 1511.06081

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

Dragos Ghioca·Khoa D. Nguyen·Hexi Ye
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Abstract

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 respect to an algebraic dynamical system, combined with a theorem of Levin regarding symmetries of the Julia set. Using a specialization theorem of Yuan and Zhang, we prove the Dynamical Manin-Mumford Conjecture for endomorhisms of P^1\times P^1 defined over the complex numbers.

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Dragos Ghioca, Khoa D. Nguyen, Hexi Ye. 2016-09-22. The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps. https://arxiv.org/abs/1511.06081

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