2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67965We study the Ruelle dynamical determinant of a real analytic diffeomorphism on a compact surface, assuming that the tangent space over the nonwandering set admits a dominated splitting. Combining previous work of Pujals and Sambarino with methods introduced by Rugh, we show that the determinant is either entire or holomorphic in a (possibly multiply) slit plane.Revised version, some mistakes corrected (e.g. in Section 3)Dynamical Systems37C30, 37D30, 37E30text