A normally elliptic Hamiltonian bifurcation
This work mainly deals with 4-dimensional autonomous Hamiltonian systems in a neighborhood of a degenerate equilibrium, with a double eigenvalue zero (and a purely imaginary pair of eigenvalues). The principal result describes the generic unfoldings of an integrable Hamiltonian, where the parameter space has dimension 3 or 1 depending on whether the linearization is semisimple or not. This uses singularity theory in the planar case. The general non-integrable case is discussed as a perturbation problem, a.o. in the light of a formal reduction to a Hamiltonian normal form.
scientific article; zbMATH DE number 409588
scientific article