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Hopf bifurcation with SN-symmetry
CMUP and Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
CMUP and Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
2009 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 22, no 3, 627-666 p.Article in journal (Refereed) Published
Abstract [en]

We study Hopf bifurcation with SN-symmetry for the standard absolutely irreducible action of SN obtained from the action of SN 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 SN × S1. We use this classification to prove the existence of branches of periodic solutions with C-axial symmetry in systems of ordinary differential equations with SN-symmetry posed on a direct sum of two such SN-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 SN × S1-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.

Place, publisher, year, edition, pages
2009. Vol. 22, no 3, 627-666 p.
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-71080DOI: 10.1088/0951-7715/22/3/007ISI: 000263259400007OAI: oai:DiVA.org:kth-71080DiVA: diva2:486501
Note
QC 20120131Available from: 2012-01-30 Created: 2012-01-30 Last updated: 2017-12-08Bibliographically approved

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