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arXiv · 1506.02144

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

Razvan M. Tudoran
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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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Razvan M. Tudoran. 2015-06-06. Asymptotic stabilization with phase of periodic orbits of three-dimensional Hamiltonian systems. https://doi.org/10.1016/j.geomphys.2017.07.001

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