Hopf bifurcation with S-N-symmetry

• Type: Article in International Scientific Journal
• Date: 2009

Authors

dias, aps (Author) FCUP; rodrigues, a (Author) Other

Journal

Title: Nonlinearity

Vol. 22 No. 2

Pages: 627-666

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 14 Citations

Scopus - 16 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-N0M

DOI: 10.1088/0951-7715/22/3/007

Abstract (EN): We study Hopf bifurcation with S-N-symmetry for the standard absolutely irreducible action of S-N obtained from the action of S-N by permutation of N coordinates. Stewart (1996 Symmetry methods in collisionless many-body problems, J. Nonlinear Sci. 6 543-63) obtains a classification theorem for the C-axial subgroups of S-N x S-1. We use this classification to prove the existence of branches of periodic solutions with C-axial symmetry in systems of ordinary differential equations with S-N-symmetry posed on a direct sum of two such S-N-absolutely irreducible representations, as a result of a Hopf bifurcation occurring as a real parameter is varied. We determine the ( generic) conditions on the coefficients of the fifth order S-N x S-1-equivariant vector field that describe the stability and criticality of those solution branches. We finish this paper with an application to the cases N = 4 and N = 5.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 40