$N$ -体问题的优级数
Majorant series for the $N$-body problem
摘要：
作为作者以前工作的后续，本文考虑了{\em引力} $N$ -体问题的{\em统一整体时间重整化函数}。它改进了收敛半径的估计，其中获得了使用一种完全不同的技术，无论是对原方程的解决方案和重正化的解决方案。建立新估计的上述技术被称为{ \em majorants}，并且允许对幂级数进行简单运算的简单应用。这样得到的新的收敛半径大约是我们以前估计的两倍。此外，我们还表明，{ \em majorants}也可以被构造来估计局部误差的{ \em隐式中点规则}（类似的龙格-库塔法）时，适用于时间重整化的$N$体方程和说明我们的结果太阳系的数值模拟的兴趣。
英文摘要：
As a follow-up of a previous work of the authors, this work considers {\em uniform global time-renormalization functions} for the {\em gravitational} $N$-body problem. It improves on the estimates of the radii of convergence obtained therein by using a completely different technique, both for the solution to the original equations and for the solution of the renormalized ones. The aforementioned technique which the new estimates are built upon is known as {\em majorants} and allows for an easy application of simple operations on power series. The new radii of convergence so-obtained are approximately doubled with respect to our previous estimates. In addition, we show that {\em majorants} may also be constructed to estimate the local error of the {\em implicit midpoint rule} (and similarly for Runge-Kutta methods) when applied to the time-renormalized $N$-body equations and illustrate the interest of our results for numerical simulations of the solar system.
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