# Linear Hamiltonian Hopf bifurcation for point group invariant perturbations of the 1:1:1 resonance

K. Efstathiou, D.A. Sadovskií and R.H. Cushman

Proc. Roy. Soc. London Ser. A, **459**(2040), pp. 2997-3019, 2003

DOI: 10.1098/rspa.2003.1158

## Abstract

We consider G × R-invariant Hamiltonians H on complex projective 2-space, where G is a point group and R is the time-reversal group. We find the symmetry-induced stationary points of H and classify them in terms of their linear stability. We then determine those points that can undergo a linear Hamiltonian Hopf bifurcation.