Global generic dynamics close to symmetry

• Tipo: Artigo em Revista Científica Internacional
• Data: 2012

Autores

Isabel S Labouriau (Autor) FCUP; Alexandre A P Rodrigues (Autor) FCUP

Revista

Título: Journal of Differential Equations

Vol. 253

Páginas: 2527-2557

ISSN: 0022-0396

Editora: Elsevier

Indexação

ISI Web of Knowledge - 20 Citações

Scopus - 18 Citações

SciELO - Scientific Electronic Library Online

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-002-4FC

DOI: 10.1016/j.jde.2012.06.009

Abstract (EN): Our object of study is the dynamics that arises in generic perturbations of an asymptotically stable heteroclinic cycle in S-3. The cycle involves two saddle-foci of different type and is structurally stable within the class of (Z(2) circle plus Z(2))-symmetric vector fields. The cycle contains a two-dimensional connection that persists as a transverse intersection of invariant surfaces under symmetry-breaking perturbations. Gradually breaking the symmetry in a two-parameter family we get a wide range of dynamical behaviour: an attracting periodic trajectory; other heteroclinic trajectories; homoclinic orbits; n-pulses; suspended horseshoes and cascades of bifurcations of periodic trajectories near an unstable homoclinic cycle of Shilnikov type. We also show that, generically, the coexistence of linked homoclinic orbits at the two saddle-foci has codimension 2 and takes place arbitrarily close to the symmetric cycle.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 31