2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140765In this paper, we give an explicit criterion when a rational holomorphic map between balls is equivalent to a polynomial holomorphic map. Making use of this criterion, we show that any proper rational holomorphic map from B^2 into B^N of degree two is equivalent to a polynomial holomorphic map; we also construct rational holomorphic maps of degree 3 that are almost linear but are not equivalent to polynomial holomorphic maps.13 pages. Dedicated to Professor J. Kohn on the occasion of his 75th birthdayComplex Variablestext