Covering relations and the existence of topologicallynormally hyperbolic invariant sets

Maciej J. Capiński

doi:10.3934/dcds.2009.23.705

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2009, Volume 23, Issue 3: 705-725. Doi: 10.3934/dcds.2009.23.705

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Covering relations and the existence of topologically normally hyperbolic invariant sets

Maciej J. Capiński^1,

1.
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków

Received: January 31, 2008

Revised: July 31, 2008

Published: August 2009

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Abstract

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.

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

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