论文标题
庞加莱在天体力学上工作：在受限制的三体问题的背景下可预测性与确定性
Poincaré Work on Celestial Mechanics: Predictability versus Determinism in the Context of Restricted Three-Body Problem
论文作者
论文摘要
牛顿在1678年发表的Mathematica Princionia Mathematica发表了《天体运动法》，这是经典力学的特征。此后，从已知的初始条件中搜索这些身体的运动很有意义，尤其是在3身体问题中。在本文中，基于确定性混乱理论的开头，基于几种新的定性工具的开发，就在1880年的庞加莱工作的影响下，揭示了这个问题。这种工具的应用使他发现了一种特殊的行为：动力不稳定。与1963年洛伦兹首先证明了这种行为的共同观念相反，庞加莱理论研究对混乱的确定性行为的存在足够清楚。直到庞加莱的时代，就有一个隐性的假设，即输出的不确定性并不是由于动态定律的任何随机性而引起的，因为它们是完全确定性的，而是由于最初条件中缺乏无限准确性。在本文中，强调确定性和可预测性的问题是不同的。
The publication of Principia Mathematica in 1678 by Newton became known the celestial bodies motion laws, which characterize the Classical Mechanics. Thereafter made sense to search about the movement of these bodies from known initial conditions, particularly in the 3 body problem. In this paper it is exposed the influence of Poincaré work, in 1880, in this problem on the beginning of Deterministic Chaos Theory based on the development of several new qualitative tools. The application of such tools led him to the discovery of a special kind of behavior: the dynamical instability. Contrary to the common idea that this kind of behavior was first evidenced by Lorenz in 1963, the Poincaré theoretical research was sufficiently clear about the existence of chaotic deterministic behavior. Until the time of Poincaré, there was a tacit assumption that the uncertainty in the output does not arise from any randomness in the dynamical laws, since they are completely deterministic, but rather from the lack of the infinite accuracy in the initial conditions. In this paper it is emphasized that the issues of determinism and predictability are distinct.
