2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62261We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.12 pagesDynamical SystemsMathematical Physics37B20Recurrence, dimensions and Lyapunov exponentstext