Hopf bifurcation with S-N-symmetry

• Tipo: Artigo em Revista Científica Internacional
• Data: 2009

Autores

dias, aps (Autor) FCUP; rodrigues, a (Autor) Outra

Revista

Título: Nonlinearity

Vol. 22 Nº 2

Páginas: 627-666

ISSN: 0951-7715

Editora: Institute of Physics Publishing

Indexação

ISI Web of Knowledge - 14 Citações

Scopus - 16 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 40