2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162057In this paper we give a characterization of the Gromov hyperbolicity of trains (a large class of Denjoy domains which contains the flute surfaces) in terms of the behavior of a real function. This function describes somehow the distances between some remarkable geodesics in the train. This theorem has several consequences; in particular, it allows to deduce a result about stability of hyperbolicity, even though the original surface and the modified one are not quasi-isometric.23 pages, 1 latex file, 2 eps figuresComplex VariablesMetric Geometry41A10, 46E35, 46G10text