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arXiv · 1511.08643

Is there switching without suspended horseshoes?

Alexandre Rodrigues
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Abstract

In general, infinite switching behaviour near networks is associated with the existence of suspended horseshoes. Trajectories that realize switching lie within these transitive sets. In this note, revisiting the equivariant Shilnikov scenario, we describe an attracting homoclinic network exhibiting forward switching and without suspended horseshoes in its neighbourhood. Thus we provide an example of an asymptotically stable network exhibiting sensitive dependence on initial conditions.

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Alexandre Rodrigues. 2015-11-27. Is there switching without suspended horseshoes?. https://arxiv.org/abs/1511.08643

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