聚焦双曲分支的平面可积开普勒台球动力学
Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch
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中文总结 AI 辅助
本文研究以聚焦双曲分支为边界的平面开普勒台球的可积动力学，利用焦点-焦散圆识别椭圆曲线并线性化动力学，分析周期轨道的凯莱条件，并推广至抛物弧和直线边界情况。
中文摘要 AI 辅助
我们考虑以开普勒中心为焦点的双曲线分支为边界的平面开普勒台球的可积动力学。作为我们先前工作\cite{JZ2}的续篇，我们利用焦点-焦散圆的存在性来识别一条椭圆曲线，在该曲线上动力学被线性化，并在此背景下分析$n$周期轨道的凯莱条件。通过取各种极限，我们还讨论了边界为聚焦抛物弧以及直线的平面开普勒台球的动力学。在最后一种情况下，我们的方法提供了不同于\cite{Felder}的推导椭圆曲线的方式。
英文摘要
We consider the integrable dynamics of a planar Kepler billiard in the plane bounded by a branch of a hyperbola focused at the Kepler center. As a sequel to our previous work \cite{JZ2}, we use the existence of the foci-caustic circle to identify an elliptic curve on which the dynamics is linearized and we analyze Cayley's condition on $n$-periodic orbits in this setting. By taking various limits also we discuss the dynamics of planar Kepler billiards with boundary being a focused parabolic arc, as well as a straight line. In this last case, our approach offers a different way to deduce the elliptic curve as in \cite{Felder}.
发表机构
- Gymnasium Holzkirchen（霍尔茨基兴中学）
- School of Mathematical Sciences, Dalian University of Technology（大连理工大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
