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Covering relations and the existence of topologically
normally hyperbolic invariant sets
We present a topological method for the detection of normally hyperbolic
type invariant sets for maps. The invariant set covers a sub-manifold without a boundary in $\mathbb{R}^k$. For the method to hold we
only need to assume that the movement of the system transversal to the
manifold has directions of topological expansion and contraction. The
movement in the direction of the manifold can be arbitrary. The result is
based on the method of covering relations and local Brouwer degree theory.