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Author(s): Manuela A. D. Aguiar
Sofia B. S. D. Castro
Labouriau, IS
Title: Dynamics near a heteroclinic network
Issue Date: 2005
Abstract: We study the dynamical behaviour of a smooth vector field on a 3-manifoldnear 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 suspendedhorseshoes 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 we have observed, numerically, the existence of such a network.
Document Type: Artigo em Revista Científica Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional
FEP - Artigo em Revista Científica Internacional

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