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Hopf bifurcation for equivariant conservative and time-reversible systems

Published online by Cambridge University Press:  14 November 2011

A. Vanderbauwhede
A. Vanderbauwhede
Affiliation:
Instituut voor theoretische mechanika, Rijksuniversiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium
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Synopsis

We study the bifurcation of small periodic solutions at a non-semi-simple 1:1-resonance in equivariant conservative or equivariant time-reversible systems. By using an equivariant Liapunov-Schmidt method and restricting to solutions with an appropriate isotropy, we reduce the problem to a scalar bifurcation equation. The analysis of this equation shows a bifurcation behaviour similar to that found for the Hamiltonian Hopf bifurcation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 103 - 128
Copyright
Copyright © Royal Society of Edinburgh 1990

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