论文标题
重力$ n $ - 体育问题的全球时间符号化
Global time-renormalization of the gravitational $N$-body problem
论文作者
论文摘要
这项工作考虑了{\ em Repitations} $ n $ body问题，并引入了全局时间 - 纯正{\ em函数}，该{\ em函数}允许与固定的时间步长有效的数值集成。首先，得出了溶液与原始方程的收敛半径的下限，这表明适当的时间符号化。在新的虚拟时间$τ$中，然后证明所有解决方案都存在于\ mathbb {r} $中的所有$τ\，并且它作为固定宽度的带状函数被唯一地扩展到固定宽度。作为副产品，获得了$ n $ - 体育问题解决方案的全球功率系列表示。值得注意的是，当其中一个群众消失时，我们的全球时间份量化仍然有效。最后，数值实验显示了一些$ n $ body遇到的问题的新时间 - 肾上风函数的效率。
This work considers the {\em gravitational} $N$-body problem and introduces global time-renormalization {\em functions} that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-renormalization. In the new fictitious time $τ$, it is then proved that any solution exists for all $τ\in \mathbb{R}$, and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the $N$-body problem is obtained. Noteworthy, our global time-renormalizations remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-renormalization functions for some $N$-body problems with close encounters.
