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Hopf bifurcation in the presence of symmetryGroup theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.
Document ID
19850043766
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Golubitsky, M.
(Houston, University Houston, TX, United States)
Stewart, I.
(Warwick, University Coventry, United Kingdom)
Date Acquired
August 12, 2013
Publication Date
January 1, 1985
Publication Information
Publication: Archive for Rational Mechanics and Analysis
Volume: 87
Issue: 2 19
ISSN: 0003-9527
Subject Category
Numerical Analysis
Accession Number
85A25917
Funding Number(s)
CONTRACT_GRANT: NSF MCS-81-01580
CONTRACT_GRANT: NAG2-279
Distribution Limits
Public
Copyright
Other

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