On the structure of uniformly hyperbolic chain control sets

Christoph Kawan

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arXiv · 1510.02042

On the structure of uniformly hyperbolic chain control sets

Christoph Kawan

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Abstract

We prove the following theorem: Let Q be an isolated chain control set of a control-affine system on a smooth compact manifold M. If Q is uniformly hyperbolic without center bundle, then the lift of Q to the extended state space U x M, where U is the space of control functions, is a graph over U. In other words, for every control u in U there is a unique x in Q such that the corresponding state trajectory phi(t,x,u) evolves in Q.

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Christoph Kawan. 2015-10-07. On the structure of uniformly hyperbolic chain control sets. https://arxiv.org/abs/1510.02042

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