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arXiv · 0905.0334

Dynamics near the p : -q Resonance

Sven Schmidt·Holger R. Dullin
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Abstract

We study the dynamics near the truncated p : +/- q resonant Hamiltonian equilibrium for p, q coprime. The critical values of the momentum map of the Liouville integrable system are found. The three basic objects reduced period, rotation number, and non-trivial action for the leading order dynamics are computed in terms of complete hyperelliptic integrals. A relation between the three functions that can be interpreted as a decomposition of the rotation number into geometric and dynamic phase is found. Using this relation we show that the p : -q resonance has fractional monodromy. Finally we prove that near the origin of the 1 : -q resonance the twist vanishes.

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Sven Schmidt, Holger R. Dullin. 2009-05-04. Dynamics near the p : -q Resonance. https://doi.org/10.1016/j.physd.2010.06.012

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