轴对称1：1：-2共振的分岔和单值性
Bifurcations and Monodromy of the Axially Symmetric 1:1:-2 Resonance
摘要：
本文研究三自由度可积哈密顿系统在1：1：-2共振椭圆平衡点附近的情形。可积性源于沿二次部分的周期运动的平均和关于垂直轴的强制旋转对称。引入一个失谐参数，我们发现一个丰富的分支图，包含三个抛物线的哈密顿Hopf分支加入在原点。我们描述了所得到的分歧3-torus丛的单值性作为失谐参数的变化，使系统通过1：1：-2共振。
英文摘要：
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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