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𝔻n-forced symmetry breaking of 𝕆(2)-equivariant problems

Published online by Cambridge University Press:Β  12 July 2007

Jacques-Elie Furter  and
Angela Maria Sitta
Jacques-Elie Furter
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK ([email protected])
Angela Maria Sitta
Affiliation:
Departamento de MatemΓ‘tica, IBILCE-UNESP, Rua CristovΓ’o Colombo 2265, SΓ£o JosΓ© do Rio Preto, Brazil ([email protected])
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Abstract

We use singularity theory to classify forced symmetry-breaking bifurcation problems where f1 is 𝕆(2)-equivariant and f2 is 𝔻n-equivariant with the orthogonal group actions on z ∈ ℝ2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1185 - 1218
Copyright
Copyright Β© Royal Society of Edinburgh 2002

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