Magnetic flows on homogeneous spaces
Magnetic flows on homogeneous spaces
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均匀空间上的磁流
DOI：
10.4171/cmh/139
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发表时间：
2006
影响因子：
0.9
通讯作者：
B. Jovanović
中科院分区：
文献类型：
--
作者：
A. Bolsinov;B. Jovanović
本文研究了一类齐性空间上正规度量的磁测地线流，特别是紧李群的（余）伴随轨道。我们给出了流的非交换可积性的证明，并显示，此外，对于（共）伴随轨道的情况下，通常的刘维尔可积性通过解析积分。我们还考虑了伴随轨道上的势系统，它是磁球摆的推广。对于紧半单李群的任意伴随轨道，证明了该系统的完全可积性。出现在《数学评论》中
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, which are generalizations of the magnetic spherical pendulum. The complete integrability of such system is proved for an arbitrary adjoint orbit of a compact semisimple Lie group. to appear in Commentarii Mathematici Helvetici