On the behavior of Mahler's measure under iteration

Paul Fili, Lukas Pottmeyer, Mingming Zhang

For an algebraic number $\alpha$ we denote by $M(\alpha )$ the Mahler measure of $\alpha$. As $M(\alpha )$ is again an algebraic number (indeed, an algebraic integer), $M(\cdot )$ is a self-map on $\over…