齐性空间上测地线流的积分：野李群的情形
Integration of geodesic flows on homogeneous spaces: the case of a wild lie group
摘要：
本文给出了具有不变度量和中心度量的齐性空间$M$上测地线流的求积可积的充要条件。建议的集成算法包括在使用一个特殊的正则变换空间$T^*M$的基础上构建的正则坐标的轨道上的coadjoint表示和单张的泊松代数的不变函数。该算法适用于积分野李群的齐性空间上的测地线流。
英文摘要：
We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces $M$ with invariant and central metrics. The proposed integration algorithm consists in using a special canonical transformation in the space $T^*M$ based on constructing the canonical coordinates on the orbits of the coadjoint representation and on the simplectic sheets of the Poisson algebra of invariant functions. This algorithm is applicable to integrating geodesic flows on homogeneous spaces of a wild Lie group.
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