2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127099Let 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.29 pagesNumber TheoryDynamical Systems11G50; 11J68, 37F10text