2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200298The dynamical system for the zero modes of the Liouville Model, which is separated from the full dynamics for the discrete shifts of time $ t \to t + π$, is investigated. The structure of the modular double in quantum case is introduced.15 pagesHigh Energy Physics - TheoryQuantum AlgebraDiscrete evolution for the zero-modes of the Quantum Liouville Modeltext