Author(s):
Manuela A. D. Aguiar 
; Sofia B. S. D. Castro ; Isabel S. Labouriau
Date: 2006
Persistent ID: http://hdl.handle.net/10216/68929
Origin: Repositório Aberto da Universidade do Porto
Document details
Simple vector fields with complex behaviour
Description
We construct symmetric polynomial vector fields in R^4 amenable to analytic proof of properties that guarantee the existence of complex behaviour. The examples possess heteroclinic networks producing switching and nearby suspended horseshoes. The heteroclinic networks in our examples are persistent under symmetry preserving perturbations. We prove that some of the connections in the networks are the transverse intersection of invariant manifolds. The remaining connections are symmetry-induced. The networks lie in an invariant three-sphere and may involve connections exclusively between equilibria or between equilibria and periodic trajectories. The same construction technique may be applied to obtain other examples with similar features.
We construct symmetric polynomial vector fields in R^4 amenable to analytic proof of properties that guarantee the existence of complex behaviour. The examples possess heteroclinic networks producing switching and nearby suspended horseshoes. The heteroclinic networks in our examples are persistent under symmetry preserving perturbations. We prove that some of the connections in the networks are the transverse intersection of invariant manifolds. The remaining connections are symmetry-induced. The networks lie in an invariant three-sphere and may involve connections exclusively between equilibria or between equilibria and periodic trajectories. The same construction technique may be applied to obtain other examples with similar features.
Document Type
Article
Language Portuguese
Language Portuguese
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