Hamiltonian Hopf bifurcation with symmetry

1 November 1990

journal article
Published by IOP Publishing in Nonlinearity

Vol. 3 (4) , 1041-1056
https://doi.org/10.1088/0951-7715/3/4/005

Abstract

Studies Hamiltonian Hopf bifurcation in the presence of a compact symmetry group G. The author classifies the expected actions of G and show that near four-dimensional fixed point subspaces of subgroups of G*Sⁱ the bifurcation of periodic solutions is diffeomorphic to the standard Hamiltonian Hopf bifurcation in two degrees of freedom. Examples are given of O(2), SO(2) and SU(2) symmetry. Furthermore it is shown that Hamiltonian Hopf bifurcation with SO(2) symmetry occurs in the Euler-Poisson equations for the Lagrange rigid body motion.

Keywords

This publication has 3 references indexed in Scilit:

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Generic bifurcation of Hamiltonian systems with symmetry
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