Dynamics near a heteroclinic network

@inproceedings{Aguiar2004DynamicsNA,
  title={Dynamics near a heteroclinic network},
  author={Manuela A. D. Aguiar and Sofia B. S. D. Castro and Isabel S. Labouriau},
  year={2004}
}
We study the dynamical behaviour of a smooth vector field on a three-manifold near a heteroclinic network. Under some generic assumptions on the network, we prove that every path on the network is followed by a neighbouring trajectory of the vector field—there is switching on the network. We also show that near the network there is an infinite number of hyperbolic suspended horseshoes. This leads to the existence of a horseshoe of suspended horseshoes with the shape of the network. Our results… CONTINUE READING
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