Dynamics near a heteroclinic network

• Tipo: Artigo em Revista Científica Internacional
• Data: 2005

Autores

Manuela A. D. Aguiar (Autor) FEP; Sofia B. S. D. Castro (Autor) FEP; Labouriau, IS (Autor) FCUP

Revista

Título: Nonlinearity

Vol. 18 Nº 1

Páginas: 391-414

ISSN: 0951-7715

Editora: Institute of Physics Publishing

Indexação

ISI Web of Knowledge - 43 Citações

Scopus - 43 Citações

Outras Informações

ID Authenticus: P-000-6BY

DOI: 10.1088/0951-7715/18/1/019

Abstract (EN): 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 we have observed, numerically, the existence of such a network.

Idioma: Português

Tipo (Avaliação Docente): Científica

Nº de páginas: 25