The linearized Poincaré map of a periodic orbit of a completely integrable Hamiltonian system is examined in the light of the finer description we get by using coordinate changes in the Lagrangian odd symplectic group. In particular, we obtain non-eigenvalue invariants called moduli. These invariants are surprisingly subtle to calculate even in the case of the geodesic flow on a 2-sphere, and reveal dynamic-geometric information that is otherwise symplectically invisible.

中文翻译：

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球上的两个动作角惊喜

根据我们通过使用拉格朗日奇辛群中的坐标变化获得的更好的描述，对完全可积的哈密顿系统的一个周期轨道的线性庞加莱图进行了检验。特别是，我们获得了称为moduli的非特征值不变式。即使在2球上的测地流的情况下，这些不变量也令人惊讶地微妙地计算出来，并显示出动态几何信息，而这些信息在几何上是看不见的。