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Dynamics near a heteroclinic network

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

Abstract

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:10.1.1.160.4590
Provided by: CiteSeerX
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