Meromorphic degeneration of rational functions over snc models of the projective line

Abstract

For an analytic family $\{f_t\}_{t\in\mathbb{D}^*}$ on the unit punctured disk that meromorphically degenerates at the origin, we show that its limiting measure on an snc model is given by the push forward of the canonical measure attached to the non-archimedean rational function naturally induced from the family, which is a generalization of the results by DeMarco-Faber and Okuyama.