2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57787We study the presence of a logarithmic time scale in discrete approximations of Sawtooth Maps on the 2--torus. The techniques used are suggested by quantum mechanical similarities, and are based on a particular class of states on the torus, that fulfill dynamical localization properties typical of quantum Coherent States.LaTeX, 45 pages, 5 figures. Small changes in the content, references added. To appear in J. Math. PhysMathematical PhysicsQuantum Physics37D20 (Primary); 81Q20, 81R30, 46L99 (Secondary)text