Nonlocal instabilities for the planar 3-body problem

牛顿三体问题是研究在欧几里德空间中相互吸引的三点质量在牛顿引力作用下的动力学问题。该系统的不稳定性描述是力学的经典问题之一。该项目研究太阳-木星-小行星系统模型的不稳定性，假设第三个天体（小行星）质量为零，第二个天体（木星）与第一个天体（太阳）相比很小，并且所有三个天体都在一个平面上运动。利用著名的马瑟理论，首席研究员寻求该系统不稳定性的数学证明。太阳系的稳定性是天文学和数学中的一个基本问题。人们普遍认为这个系统不稳定。作为了解物理情况的第一步，寻找太阳系数学模型中的不稳定性是极其重要的。这个项目的主要目的是试图揭示太阳-木星-小行星系统数学模型的复杂行为。这个模型的基本问题是小行星的轨道是否会不稳定（简单来说，它相对于太阳和木星的位置是否会随着时间的推移而发生很大的变化）。首席研究员将试图找到这种不稳定性，并对其进行详细的数学描述。这可能最终导致对整个太阳系的不稳定性有更深入的了解，因为太阳和木星是太阳系中对大多数行星运动影响最大的天体。

The Newtonian three-body problem consists in studying the dynamics of three point masses moving in Euclidean space and mutually attracted under Newtonian gravitation. The description of instabilities in this system is one of the classical problems of mechanics. This project investigates instabilities for the model of the Sun-Jupiter-Asteroid system, assuming that the third body (the asteroid) has zero mass, that the second (Jupiter) is tiny in comparison with the first (the Sun), and that all three bodies move in a plane. Using the well-known Mather theory, the principal investigator seeks a mathematical proof of instability for this system. The stability of the Solar System is a fundamental issue in astronomy and mathematics. The general belief is that the system is not stable. As a first step toward understanding the physical situation it is extremely important to look for instabilities within mathematical models of the Solar System. The main thrust of this project represents an attempt to shed light on the complicated behavior of a mathematical model for the Sun-Jupiter-Asteroid system. The fundamental question for this model is whether a trajectory of the asteroid can be unstable (in oversimplified terms, whether its positions relative to the Sun and Jupiter can change a great deal over time). The principal investigator will try to find such instabilities and give a detailed mathematical description of them. This could eventually lead to a deeper understanding of instabilities in the entire Solar System, since the Sun and Jupiter are the bodies in it that have the largest impact on the motion of most of the planets.