2024/10/02 by Tobias Våge Henriksen, Henriksen, Tobias Våge · 1 citation
Mathematics · Physics and Astronomy · #37J35 53D20 70H06 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2410.01372
openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that su(2) rational and trigonometric Gaudin models, or in other words, generalised coupled angular momenta systems, have singularities that undergo Hamiltonian Hopf bifurcations. In particular, we find a normal form for the Hamiltonian Hopf bifurcation up to sixth order, letting us determine when the bifurcation is degenerate or not. Furthermore, in the non-degenerate case we may use the fourth order terms to determine whether the bifurcation is supercritical or subcritical; whether a flap appears in the image of the momentum map or not. Finally, figures illustrating some of the bifurcations taking place in su(2) Gaudin models are presented, showing that there are more bifurcations occurring than only Hamiltonian Hopf ones.