Dynamics near a heteroclinic network

• Type: Article in International Scientific Journal
• Date: 2005

Authors

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

Journal

Title: Nonlinearity

Vol. 18 No. 1

Pages: 391-414

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 43 Citations

Scopus - 43 Citations

Other information

Authenticus ID: 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.

Language: Portuguese

Type (Professor's evaluation): Scientific

No. of pages: 25