2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157342We show that invariant submanifolds with boundary, and more generally with corners which are normally expanded by an endomorphism are persistent as $a$-regular stratifications. This result will be shown in class $C^s$, for $s\ge 1$. We present also a simple example of a submanifold with boundary which is normally expanded but non-persistent as a differentiable submanifold.Dynamical Systemstext