Dynamics near the p : -q Resonance

Details Dynamics near the p : -q Resonance Dynamics near the p : -q Resonance

2009-05-04

arxiv.org/abs/0905.0334v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, 3 figures

Scientific paper

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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