Autor(es):
Manuela A. D. Aguiar 
; Sofia B. S. D. Castro ; Isabel S. Labouriau
Data: 2006
Identificador Persistente: http://hdl.handle.net/10216/68929
Origem: Repositório Aberto da Universidade do Porto
Detalhes do Documento
Simple vector fields with complex behaviour
Descrição
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.
Tipo de Documento
Artigo
Idioma Português
Idioma Português
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