2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75776In 1970, Hirsch asked what kind of compact invariant sets could be part of a hyperbolic set. Here we obtain that, in case such an invariant set is a 3D manifold, it is a connected sum of tori with handles quotiented by involutions. Moreover, if the manifold is orientable, the involutions are all trivial. In 1975, Ma{ñ}{é} characterized hyperbolic dynamics restricted to manifolds and called them quasi Anosov. We also classify here quasi-Anosov dynamics in 3D-manifolds.4 pagesDynamical Systems37D05; 37D20text