Degenerate Hamiltonian Hopf bifurcations. (English) Zbl 0853.58053

van der Meer, J. C.

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)

MSC:

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

Keywords:

Hamiltonian system; singularity theory; bifurcation