论文标题
绝对的周期性台球轨道任意高秩序
Absolutely Periodic Billiard Orbits of Arbitrarily High Order
论文作者
论文摘要
我们表明，对于任何自然数n，包含绝对周期性轨道N的域集合在具有光滑边界的严格凸面域中密集。这种轨道存在的证明是贡献轨道图的台球图的延伸。我们的结果是朝着反驳一个猜想的一步，即欧几里得台球中没有绝对的周期性台球轨道，也表明IVRII对定期轨道措施的猜想可能不是正确的。
We show that for any natural number n, the set of domains containing absolutely periodic orbits of order n are dense in the set of bounded strictly convex domains with smooth boundary. The proof that such an orbit exists is an extension to billiard maps of the results of a paper by Gonchenko, Shilnikov, and Turaev, where it is proved that such maps are dense in Newhouse domains in regions of real-analytic area-preserving two-dimensional maps. Our result is a step toward disproving a conjecture that no absolutely periodic billiard orbits of infinite order exist in Euclidean billiards and is also an indication that Ivrii's Conjecture about the measure set of periodic orbits may not be true.
