Abstract
It is known that in one-parameter families of Hamiltonian systems purely imag-inary eigenvalues of the linearization generically split off the imaginary axis if a 1 – 1-resonance occurs. This phenomenon is also known as the Hamiltonian Hopf bifurcation, see [6]. Recently it has been shown that the situation drastically changes if the underlying system possesses symmetry (see [4], [2]). In this case, generically, the eigenvalues may also pass through 1 –1-resonances and stay on the imaginary axis. In Hamiltonian systems without any additional structure passing is a phenomenon of codimension 3 (see [3], [7]).
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