论文标题
快速驱动系统的指数稳定性，并应用于天体力学
Exponential stability of fast driven systems, with an application to celestial mechanics
论文作者
论文摘要
我们构建一种适合{\ it快速驱动系统}的正常形式。我们称之为SO系统，包括操作$ {\ rm i} $，Angles {$ψ$}和一个快速坐标$ Y $，在矢量的动作下移动 - field $ n $仅取决于$ {\ rm i} $和$ y $，并且消失了$ {\ rm i} $ - i} $ - 组成。 {在没有坐标$ y $的情况下，已经对此类系统进行了广泛的调查，众所周知，在打开小小的扰动项后，与扰动的大小相比，归一化的操作$ {\ rm i} $变化呈指数小的变化。我们获得了经典状况的相同结果，}不需要捕获参数的额外好处，因为没有小分母出现。 {我们使用结果证明，在三体问题中，某个功能的级别集称为{\ it Euler Integral}，在短时间内与碰撞紧密地呈指数级的变化。}
We construct a normal form suited to {\it fast driven systems}. We call so systems including actions ${\rm I}$, angles {$ψ$}, and one fast coordinate $y$, moving under the action of a vector--field $N$ depending only on ${\rm I}$ and $y$ and with vanishing ${\rm I}$--components. {In absence of the coordinate $y$, such systems have been extensively investigated and it is known that, after a small perturbing term is switched on, the normalised actions ${\rm I}$ turn to have exponentially small variations compared to the size of the perturbation. We obtain the same result of the classical situation, with the additional benefit that } no trapping argument is needed, as no small denominator arises. {We use the result to prove that, in the three--body problem, the level sets of a certain function called {\it Euler integral} have exponentially small variations in a short time, closely to collisions.}
