Dynamics near the p:-q resonance

作者：Schmidt Sven; Dullin Holger R^*

来源：Physica D: Nonlinear Phenomena , 2010, 239(19): 1884-1891.

DOI：10.1016/j.physd.2010.06.012

• Fractional monodromy
• Resonant oscillator
• Vanishing twist
• Singular reduction

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.

• 出版日期2010-10-1