2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62906In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.M.S. thesis. 13 pages, 1 figureAlgebraic TopologyDifferential Geometry55-02On the lower bounds for the number of periodic billiard trajectories in manifolds embedded in Euclidean spacetext