Knauf Andreas
Department of Mathematics, Friedrich-Alexander-University Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany
Philos Trans A Math Phys Eng Sci. 2018 Sep 17;376(2131):20170426. doi: 10.1098/rsta.2017.0426.
Asymptotic velocity is defined as the Cesàro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in celestial mechanics with four or more bodies. Here, we show for a class of pair potentials including the homogeneous ones of degree - for ∈(0, 2), that asymptotic velocities exist for up to four bodies, dimension three or larger, for any energy and initial conditions on the energy surface.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.
渐近速度被定义为速度的切萨罗极限。因此，对于有界相互作用势，其存在性已得到证明。在有四个或更多天体的天体力学中，已知这是错误的。在此，我们表明，对于一类包括次数为 - （其中 ∈(0, 2)）的齐次势的对势，对于三维或更高维中多达四个天体的情况，在能量表面上的任何能量和初始条件下，渐近速度都存在。本文是主题为“有限维可积系统：新趋势和方法”的一部分。
