Global generic dynamics close to symmetry

• Type: Article in International Scientific Journal
• Date: 2012

Authors

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

Journal

Title: Journal of Differential Equations

Vol. 253

Pages: 2527-2557

ISSN: 0022-0396

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 20 Citations

Scopus - 18 Citations

SciELO - Scientific Electronic Library Online

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 31