Covering relations and the existence of topologically normally hyperbolic invariant sets

Abstract

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