Computation of magnetic coordinates and action-angle variables

We have developed a new algorithm for calculating magnetic surfaces and coordinates for a given three-dimensional magnetic field. The algorithm serves also to solve the equivalent problem of computing invariant tori and action-angle variables for a one-dimensional time-dependent numerically specified Hamiltonian (or a two-dimensional time-independent Hamiltonian). Our approach combines features of both iterative and trajectory following methods. This allows us to overcome the inefficiency of trajectory following methods near low order rational surfaces, while retaining some of the robustness of these methods.