2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126576In this paper we show that the quotient Aubry set associated to certain Lagrangians is totally disconnected (i.e., every connected component consists of a single point). Moreover, we discuss the relation between this problem and a Morse-Sard type property for (difference of) critical subsolutions of Hamilton-Jacobi equations.21 pages, accepted for publication in Ergodic Theory Dynam. SystemsDynamical SystemsMathematical PhysicsAnalysis of PDEs37J50; 49L25; 58K05text