2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75937We classify the closed orbits under the action of maximal tori on the S-adic homogeneous spaces. As an application, we prove that if the set of values at the integer points of any homogeneous non-degenerate split form is discrete, then the form is multiple of a form with rational coefficients. Our result is related to the notable Littlewood conjecture.26 pagesNumber TheoryDynamical Systems11J17; 37D40text