2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66749We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of the central foliation is severely restricted. We also prove a topological analogue of this result: the intersection of every proper closed invariant subset with each central leaf is compact.28 pagesDynamical Systems37A05, 37A45, 37B05, 37C40text