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Generating functions for Hopf bifurcation with Sn-symmetry
CMUP and Dep. de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.
Centro de Matemática da Universidade do Porto (CMUP) and Dep. de Matemática Pur, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
2009 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 25, no 3, 823-842 p.Article in journal (Refereed) Published
Abstract [en]

Hopf bifurcation in the presence of the symmetric group (acting naturally by permutation of coordinates) is a problem with relevance to coupled oscillatory systems. To study this bifurcation it is important to construct the Taylor expansion of the equivariant vector field in normal form. We derive generating functions for the numbers of linearly independent invariants and equivariants of any degree, and obtain recurrence relations for these functions. This enables us to determine the number of invariants and equivariants for all , and show that this number is independent of for sufficiently large . We also explicitly construct the equivariants of degree three and degree five, which are valid for arbitrary .

Place, publisher, year, edition, pages
2009. Vol. 25, no 3, 823-842 p.
Keyword [en]
Equivariants, Generating functions, Hopf bifurcation, Invariants, Symmetric group
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-71077DOI: 10.3934/dcds.2009.25.823ISI: 000269221200005OAI: oai:DiVA.org:kth-71077DiVA: diva2:486498
Note
QC 20120131Available from: 2012-01-30 Created: 2012-01-30 Last updated: 2017-12-08Bibliographically approved

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