Wandering points for the Mahler measure

Paul Fili, Lukas Pottmeyer, Mingming Zhang

Published 2021-09-23Version 1

Mahler's measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mahler's measure. We completely solve the problem for all abelian number fields, and more generally, for all extensions of the rationals of degree at most five.