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            <title xml:lang="en">A geometrical proof of the persistence of normally hyperbolic submanifolds</title>
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              <p>We present a simple, computation free and geometrical proof of the following classical result: for a diffeomorphism of a manifold, any compact submanifold which is invariant and normally hyperbolic persists under small perturbations of the diffeomorphism. The persistence of a Lipschitz invariant submanifold follows from an application of the Schauder fixed point theorem to a graph transform, while smoothness and uniqueness of the invariant submanifold are obtained through geometrical arguments. Moreover, our proof provides a new result on persistence and regularity of ''topologically" normally hyperbolic submanifolds, but without any uniqueness statement.</p>
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