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

K. Efstathiou, D. A. Sadovskií, R. H. Cushman (2003)
Proceedings of the Royal Society A

Abstract

We consider $G times R$-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.

@article{2003_ESC_Hamiltonian_Hopf_Discrete_Symmetry,
 abstract = {We consider $G \times R$-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.},
 author = {Efstathiou, K. and Sadovskií, D. A. and Cushman, R. H.},
 doi = {10.1098/rspa.2003.1158},
 journal = {Proceedings of the Royal Society A},
 journalurl = {https://rspl.royalsocietypublishing.org/},
 number = {2040},
 pages = {2997-3019},
 title = {Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance},
 volume = {459},
 year = {2003}
}