Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems

We provide a geometric method to stabilize asymptotically with phase an arbitrary fixed periodic orbit of a locally generic three-dimensional Hamiltonian dynamical system. The main advantage of this method is that one need not to know a parameterization of the orbit to be stabilized, but only the values of the Hamiltonian and a fixed Casimir (of the Poisson configuration manifold) at that orbit. The stabilization procedure is illustrated in the case of the Rilcitalce model of geomagnetic reversal. (C) 2017 Elsevier B.V. All rights reserved.