论文标题
空间限制四个身体问题的同型动力学蓝天进入垂直Lyapunov家庭的Smale Horseshoes
Homoclinic dynamics in a spatial restricted four body problem blue skies into Smale horseshoes for vertical Lyapunov families
论文作者
论文摘要
平面等边限制的四体问题中的鞍座对焦平衡的一组横向同斜线相结合，承认某些简单的同型轨道构成了完整同层互动的骨骼，或同层同型的骨架。在目前的工作中，平面限制的四体问题被视为空间问题的不变子系统，并且从数值的角度研究了该平面同质骨架对空间动力学的影响。从垂直的lyapunov家族开始，从马鞍焦点平衡中发出，我们计算了这些空间周期性轨道的稳定/不稳定的流形，并寻找基本平面同层层次附近的这些歧管之间的相互作用。这样，我们能够将所有基本的平面同质运动运动作为空间问题，作为适当的垂直lyapunov轨道的同层次，通过Smale Tangle Therorem，这表明空间问题中存在混乱的动作。尽管平面问题中的马鞍量平衡溶液仅在一组离散的能级中发生，但空间问题中的循环到周期的同层次对于能量的微小变化而言是强大的。
The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admit certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection -- or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view. Starting from the vertical Lyapunov families emanating from saddle focus equilibria, we compute the stable/unstable manifolds of these spatial periodic orbits and look for intersections between these manifolds near the fundamental planar homoclinics. In this way, we are able to continue all of the basic planar homoclinic motions into the spatial problem as homoclinics for appropriate vertical Lyapunov orbits which, by the Smale Tangle theorem, suggest the existence of chaotic motions in the spatial problem. While the saddle-focus equilibrium solutions in the planar problems occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics in the spatial problem are robust with respect to small changes in energy.
