2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130556We give necessary and sufficient conditions of infinite determinacy for smooth function germs whose critical locus contains a given set. This set is assumed to be the zero variety X of some analytic map germ having maximal rank on a dense subset of X. We obtain a result in terms of Lojasiewicz estimates which extends, in particular, previous works by Sun & Wilson on line singularities, and by Grandjean on singularities of codimension 1 or 2.9 pages, AMS-LaTeX - cosmetic changesClassical Analysis and ODEs58K40text