Degenerate Hamiltonian Hopf bifurcations. (English) Zbl 0853.58053

Bates, Larry M. (ed.) et al., Conservative systems and quantum chaos. Based on the workshop, Waterloo, Canada, October 1992. Providence, RI: American Mathematical Society. Fields Inst. Commun. 8, 159-176 (1996).
The author deals with the problem of degenerate Hamiltonian Hopf bifurcation. Basically the approach consists of the following four steps: 1. Normal form theory for Hamiltonian vector fields. 2. Weinstein-Moser reduction. 3. Singularity theory. 4. Analysis of singularity theoretic normal form. Results concerning a complete programme for analyzing Hamiltonian bifurcation are outlined.
For the entire collection see [Zbl 0836.00034].
Reviewer: Y.Kozai (Tokyo)


37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G99 Local and nonlocal bifurcation theory for dynamical systems