Hamiltonian Double-Zero Eigenvalue

摘要

A universal local bifurcation analysis of an autonomous Hamiltonian system arounda certain equilibrium point is presented. This central equilibrium has a double zero eigenvalue, the other eigenvalues being in general position. Emphasis is given to the two degrees of freedom case where these other eigenvalues are purely imaginary. By normal form techniques and catastrophe theory unfoldings are obtained, having 'integrable' approximations related to the fold and to the elliptic and hyperbolic umbilic catastrophes.