论文标题
开普勒问题的darboux反转
Darboux inversions of the Kepler problem
论文作者
论文摘要
在1873年伯特兰德（Bertrand）提出并解决了一个著名的问题时，达伯克斯（Darboux）在1877年发现了一个抽象的革命表面家族，每个家族都具有力量功能，并具有惊人的属性，所有轨道都定期在相位空间的开放式集合中。我们对这个家庭进行了描述，解释了他们为什么拥有此属性：它们是恒定曲率表面上开普勒问题的darboux倒置。 Darboux在1889年简短地引入了我们所说的Darboux逆向，作为Goursat刚才描述的保形地图的另一种方法。
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of the phase space. We give a description of this family which explains why they have this property: they are the Darboux inverses of the Kepler problem on constant curvature surfaces. What we call the Darboux inverse was briefly introduced by Darboux in 1889 as an alternative approach to the conformal maps that Goursat had just described.
