论文标题
H. dullin和R. Montgomery的猜想证明
Proof of a conjecture by H. Dullin and R. Montgomery
论文作者
论文摘要
在准周期制度中平面欧拉问题的框架中，文献中可用的时期的公式仅在其奇异性的一侧很简单。在本文中，我们将这种公式与其他公式进行补充，这在另一侧更简单。这种新公式的推导使用开普勒限制和复杂的分析工具。 作为一种应用，我们证明了H. dullin和R. Montgomery的猜想，该猜想指出，这种时期及其比率{\ it旋转数}是其非平地第一积分的单调函数，在任何固定的能级上。
In the framework of the planar Euler problem in the quasi--periodic regime, the formulae of the periods available in the literature are simple only on one side of their singularity. In this paper, we complement such formulae with others, which result simpler on the other side. The derivation of such new formulae uses the Keplerian limit and complex analysis tools. As an application, we prove a conjecture by H. Dullin and R. Montgomery, which states that such periods, as well as their ratio, the {\it rotation number}, are monotone functions of their non--trivial first integral, at any fixed energy level.
