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In this paper we give a characterization of the Gromov hyperbolicity oftrains (a large class of Denjoy domains which contains the flute surfaces) interms of the behavior of a real function. This function describes somehow thedistances between some remarkable geodesics in the train. This theorem hasseveral consequences; in particular, it allows to deduce a result aboutstability of hyperbolicity, even though the original surface and the modifiedone are not quasi-isometric.

A real variable characterization of Gromov hyperbolicity of flute surfaces