  Let g be a nonconstant rational map from the projective line to itself that
has degree greater than one and is defined over a number field. The map g gives
rise to generalized Mahler measures for polynomials in one variable. We use
diophantine approximation to show that the generalized Mahler measure of a
polynomial F at a place v can be computed by averaging the log of the v-adic
absolute value of F over the periodic points of g. This allows us to compute
canonical heights of algebraic points via equidistribution on periodic points.
