American Institute of Mathematical Sciences

Advanced
July  2009, 23(3): 705-725. doi: 10.3934/dcds.2009.23.705

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, Poland

Received  February 2008 Revised  August 2008 Published  November 2008

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.
Keywords: Normally hyperbolic sets, covering relations, Brouwer degree.
Mathematics Subject Classification: Primary: 34D10, 34D35; Secondary: 37C25.
Citation: Maciej J. Capiński. Covering relations and the existence of topologically normally hyperbolic invariant sets. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 705-725. doi: 10.3934/dcds.2009.23.705
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