2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74720We prove measurable Livsic theorems for dynamical systems modelled by Markov Towers. Our regularity results apply to solutions of cohomological equations posed on Henon-like mappings and a wide variety of nonuniformly hyperbolic systems. We consider both Holder cocycles and cocycles with singularities of prescribed order.35 pages, To be published in Ergodic Theory and Dynamical SystemsDynamical Systems37A29 (Primary) 37C15, 37D25 (Secondary)text