Detection of Generic One Parameter Bifurcations of Hamiltonian Equilibria

In this paper several possibilities are considered for constructing test functions which reveal generic one parameter bifurcations of equilibria of Hamiltonian systems. These are alternatives to computing all the eigenvalues of the linearized system. Because of the Hamiltonian structure, most test functions that are used for general systems do not work here. Typically a test function that should change sign at a bifurcation point has a multiple zero and no sign change there for Hamiltonian systems. Methods based on characteristic polynomials and bialternate products of matrices are discussed in detail.