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Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems (1506.02144v3)
Published 6 Jun 2015 in math.DS, math-ph, and math.MP
Abstract: 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 needs not 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 Rikitake model of geomagnetic reversal.
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