2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158810We establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic, using the Perron-Frobenius operator. We apply the result to asymptotically periodic transformations and give an extensive specific example of asymptotically periodic transformations by using the tent map.ProbabilityDynamical Systems28D05, 37A50, 60F05, 60F17text