2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78446We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspectives and a recent result of Hofer, Wyzsocki, and Zehnder.Dynamical SystemsGeometric Topology57M25, 76C05(primary) 58F07, 58F22 (secondary)text