2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137010We prove that a $C^2$ diffeomorphism $f$ of a compact manifold $M$ satisfies Axiom A and the strong transversality condition if and only if it is Hölder stable, that is, any $C^1$ diffeomorphism $g$ of $M$ sufficiently $C^1$ close to $f$ is conjugate to $f$ by a homeomorphism which is Hölder on the whole manifold.14 pagesDynamical Systems37C75; 37D20text