2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59365Let $T\subset \R^{m+1}$ be a strictly convex domain bounded by a smooth hypersurface $X=\partial T$. In this paper we find lower bounds on the number of billiard trajectories in $T$ which have a prescribed intial point $A\in X$, a prescribed final point $B\in X$ and make a prescribed number $n$ of reflections at the boundary $X$. We apply a topological approach based on calculation of cohomology rings of certain configuration spaces.21 pages, 1 figureDifferential GeometryAlgebraic Topology3Dxx, 58Exxtext