2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68264We prove exponential growth rate of contractible closed geodesics for an arbitrary bumpy metric on manifolds of the form X#Y, where the fundamental group of X has a subgroup of finite index at least 3 and Y is simply connected and not a homotopy sphere.There was an error in the original versionDifferential GeometryDynamical Systems53C22text