کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1893614 | 1044099 | 2007 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Geodesics on the ellipsoid and monodromy Geodesics on the ellipsoid and monodromy](/preview/png/1893614.png)
After reviewing the properties of the geodesic flow on the three-dimensional ellipsoid with distinct semi-axes, we investigate the three-dimensional ellipsoid with the two middle semi-axes equal, corresponding to a Hamiltonian invariant under rotations. The system is Liouville integrable, and symmetry reduction leads to a (singular) system on a two-dimensional ellipsoid with an additional potential and with a hard billiard wall inserted in the middle coordinate plane. We show that the regular part of the image of the energy–momentum map is not simply connected and there is an isolated critical value for zero angular momentum. The singular fibre of the isolated singular value is a doubly pinched torus multiplied by a circle. This circle is not a group orbit of the symmetry group, and thus analysis of this fibre is non-trivial. Finally we show that the system has a non-trivial monodromy, and consequently does not admit single-valued globally smooth action variables.
Journal: Journal of Geometry and Physics - Volume 57, Issue 12, December 2007, Pages 2437–2454