2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118028We construct a smooth hyperbolic volume preserving diffeomorphism on a four dimensional compact Riemannian manifold which has countably many ergodic components and is arbitrarily close to the identity map.Dynamical Systems37D25, 37D30A hyperbolic diffeomorphism with countably many ergodic components near identitytext