2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80854In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Eventhough it is part of a widely accepted belief that ellipticity implies stability, classical theorems show that the certainty of stability relies upon more fine conditions. We present a review of the main results and general theorems and describe the procedure to fullfill the supplementary conditions for strictly convex billiards.for programs see http://www.mat.ufmg.br/~syok/papersChaotic DynamicsDynamical Systemstext