论文标题
Gevrey的规律性，以正式可线化的Treschev台球
Gevrey regularity for the formally linearizable billiard of Treschev
论文作者
论文摘要
特雷斯切夫（Treschev）提出了一个非凡的发现，即存在正式的力量系列，描述了具有本地线性动力学的台球。我们表明，如果线性动力学的频率是二苯胺，则TRESCHEV示例为$（1+α）$ - gevrey，对于某些$α> 0 $。我们的证明是基于一个迭代方案，该方案进一步阐明了原始Treschev结构的结构和对称性。希望我们的结果能阐明这个示例是否融合的更重要的问题。
Treschev made the remarkable discovery that there exists formal power series describing a billiard with locally linearizable dynamics. We show that if the frequency for the linear dynamics is Diophanine, the Treschev example is $(1+ α)$-Gevrey for some $α> 0$. Our proof is based on an iterative scheme that further clarifies the structure and symmetries underlying the original Treschev construction. Hopefully, Our result sheds a light on the more important question of whether this example is convergent.
