2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111548In this article we study the existence and the continuation of periodic solutions of autonomous Newtonian systems. To prove the results we apply the infinite-dimensional version of the degree for SO(2)-equivariant gradient operators. Using the results due to Rabier we show that the Leray-Schauder degree is not applicable in the proofs of our theorems, because it vanishes.31 pagesClassical Analysis and ODEs34C25, 47H11text