论文标题
椭圆台球中自我交织的N周期不变的不变性
Invariants of Self-Intersected N-Periodics in the Elliptic Billiard
论文作者
论文摘要
我们研究了椭圆台球中的自我交织的n周期，描述了有关它们的几何形状的新事实（例如，自我交织的4个周期学具有与焦点相关的顶点）。我们还检查了一些在“椭圆台球中N-周期的新不变的新不变的”（2020年）中列出的（2020），Arxiv：2004.12497，在自我相互作用的情况下仍然不变。为此，我们为许多低N的简单和自我交织的情况提供了明确的表达。我们确定了两个特殊情况（一种简单的情况，一个自我交织），其中规定不变的数量实际上是可变的。
We study self-intersected N-periodics in the elliptic billiard, describing new facts about their geometry (e.g., self-intersected 4-periodics have vertices concyclic with the foci). We also check if some invariants listed in "Eighty New Invariants of N-Periodics in the Elliptic Billiard" (2020), arXiv:2004.12497, remain invariant in the self-intersected case. Toward that end, we derive explicit expressions for many low-N simple and self-intersected cases. We identify two special cases (one simple, one self-intersected) where a quantity prescribed to be invariant is actually variable.
