Apparaît dans la collection : Diophantine approximation and transcendence 2025 / Approximation diophantienne et transcendance 2025

The dynamical Bogomolov conjecture is a dynamical counterpart of the classical Bogomolov conjecture. Roughly speaking, it states that given a polarized endomorphism f : X → X of a projective variety and a subvariety $Z \subset X$, all defined over a number field, the subvariety contains a Zariski dense and small sequence for an appropriate canonical height function if and only if it is preperiodic - except for obvious counter-examples. In joint works with Johan Taflin, and with Johan Taflin and Gabriel Vigny, we study uniform versions of this conjecture. We prove several results. As a particular case, we provide a dynamical proof of a uniform version of a Bogomolov type statement for algebraic tori.