introduced by lehmer in 1933, the classical mahler measure of a complex rational function $p$ in one or more variables is given by integrating $\log|p(x_1, \ldots, x_n)|$ over the unit torus. lehmer asked whether the mahler measures of integer polynomials, when nonzero, must be bounded away from zero, a question that remains open to this day. in this talk we generalize mahler measure by associating it with a discrete dynamical system $f: \mathbb{c} \to \mathbb{c}$, replacing the unit torus by the $n$-fold cartesian product of the julia set of $f$ and integrating with respect to the equilibrium measure on the julia set. we then characterize those two-variable integer polynomials with dynamical mahler measure zero, conditional on a dynamical version of lehmer's conjecture.