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arXiv · 1807.09453

Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance

Konstantinos Efstathiou·Heinz Hanßmann·Antonella Marchesiello
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Abstract

We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from averaging along the periodic motion of the quadratic part and an imposed rotational symmetry about the vertical axis. Introducing a detuning parameter we find a rich bifurcation diagram, containing three parabolas of Hamiltonian Hopf bifurcations that join at the origin. We describe the monodromy of the resulting ramified 3-torus bundle as variation of the detuning parameter lets the system pass through 1:1:-2 resonance.

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Konstantinos Efstathiou, Heinz Hanßmann, Antonella Marchesiello. 2018-07-25. Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance. https://doi.org/10.1016/j.geomphys.2019.103493

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