  Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued
functions satisfying certain conditions. In this paper, we solve the inverse
problem for which recovers a Hamiltonian from the solution of a first-order
system attached to a given Hamiltonian, consisting of ordinary differential
equations parametrized by a set of complex numbers, under certain conditions
for the solutions. This inverse problem is a generalization of the inverse
problem for two-dimensional canonical systems.
