论文标题
椭圆等同步中的符号动态限制了三个身体问题
Symbolic Dynamics in the Elliptic Isosceles Restricted Three Body Problem
论文作者
论文摘要
椭圆质等这件限制了三个身体问题（REI3BP）模拟无质量体的运动，这是由牛顿引力的影响，由另外两个称为初选的身体引起的牛顿引力。质量的初选$ m_ {1} = m_ {2} $沿着其重力吸引力下的退化开普勒椭圆碰撞轨道（在一条线上）移动，而第三个无质量的粒子在平面上移动到垂直于其运动线的平面上，并穿过初处的质量中心。通过对称，无质量粒子的角动量$ g $沿原始线方向的组成部分是保守的。 我们通过在相位空间的某个子集上构建一个Smale Morseshoe，在REI3BP中显示了REI3BP中的符号动力。结果，我们推断出REI3BP具有振荡动作，即轨道，它们会留下每个有界区域，但经常返回到某个固定界面区域。证明依赖于与无穷大的不变歧管相关的横向同型连接的存在。由于无穷大的稳定和不稳定的流形之间的距离呈指数小，因此梅尔尼科夫理论不适用。
The elliptic isosceles restricted three body problem (REI3BP) models the motion of a massless body under the influence of the Newtonian gravitational force caused by two other bodies called the primaries. The primaries of masses $m_{1}=m_{2}$ move along a degenerate Keplerian elliptic collision orbit (on a line) under their gravitational attraction, whereas the third, massless particle, moves on the plane perpendicular to their line of motion and passing through the center of mass of the primaries. By symmetry, the component of the angular momentum $G$ of the massless particle along the direction of the line of the primaries is conserved. We show the existence of symbolic dynamics in the REI3BP for large $G$ by building a Smale horseshoe on a certain subset of the phase space. As a consequence we deduce that the REI3BP possesses oscillatory motions, namely orbits which leave every bounded region but return infinitely often to some fixed bounded region. The proof relies on the existence of transversal homoclinic connections associated to an invariant manifold at infinity. Since the distance between the stable and unstable manifolds of infinity is exponentially small, Melnikov theory does not apply.
