Proof of a dynamical Bogomolov conjecture for lines under polynomial actions

TL;DR

This paper proves a dynamical version of the Bogomolov conjecture for lines in affine space under polynomial actions, establishing new results in arithmetic dynamics.

Contribution

It introduces a dynamical Bogomolov conjecture for polynomial actions on lines and proves it in the special case of affine lines.

Findings

Proved the conjecture for lines in affine space under polynomial maps.

Established conditions under which points of small height are contained in special subvarieties.

Extended the understanding of dynamical systems in arithmetic geometry.

Abstract

We prove a dynamical version of the Bogomolov conjecture in the special case of lines in affine space A^m under the action of a map (f_1,...,f_m) where each f_i is a polynomial in Q-bar[X] of the same degree.