2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98987We give topological lower bounds on the number of periodic and closed trajectories in strictly convex smooth billiards. We use variational reduction admitting a finite group of symmetries and apply topological approach based on equivariant Morse and Lusternik - Schnirelman theories. The paper continues results published in math.DG/9911226 and math.DG/000604931 pages, 3 figuresAlgebraic TopologyDifferential Geometry3Dxx, 58Exxtext