Estimating Mahler measures using periodic points for the doubling map

The Mahler measure m(P)$m\left(P\right)$ of a polynomial P$P$ is a numerical value which is useful in number theory, dynamical systems and geometry. In this article we show how this can be written in terms of periodic points for the doubling map on the unit interval. This leads to an interesting algorithm for approximating m(P)$m\left(P\right)$ which we illustrate with several examples.