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Covering relations and the existence of topologically normally hyperbolic invariant sets

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  • 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.
    Mathematics Subject Classification: Primary: 34D10, 34D35; Secondary: 37C25.


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