Location of Repository

Dynamics near a heteroclinic network

By Manuela A. D, Aguiar Sofia, B. S. D. Castro and Isabel S. Labouriau


Abstract. We study the dynamical behaviour of a smooth vector field on a 3-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 are motivated by an example constructed by Field (Lectures on Bifurcations, Dynamics, and Symmetry, Pitman Research Notes in Mathematics Series 356, Longman,1996) where w

Topics: have observed, numerically, the existence of such a network
Year: 2010
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.fc.up.pt/cmup/prepr... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.