Bunimovich 体育场的无穷小动力学谱刚性
Infinitesimal dynamical spectral rigidity of the Bunimovich stadium
- University of California, Los Angeles（加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明圆形 Bunimovich 体育场在特定凸弧替换和对称条件下具有无穷小动力学谱刚性，其形变函数恒为零，且任意直边时形变函数张成有限维空间。
AI中文摘要：
我们证明了具有足够长直边的圆形 Bunimovich 体育场在由严格凸的 $C^{4}$ 弧替换其两个圆弧并保持关于平行于直边的轴对称的域类中的无穷小动力学谱刚性。即，如果此类中通过体育场的 $C^{1}$ 单参数族保持长度谱，那么其在体育场处的形变函数恒为零。对于任意长度的直边，此类族的形变函数仍然张成一个有限维空间。
英文摘要：
We prove the infinitesimal dynamical spectral rigidity of the circular Bunimovich stadium with sufficiently long flat edges, in the class of domains obtained by replacing its two circular arcs with strictly convex $C^{4}$ arcs and keeping its reflection symmetry across the axis parallel to the flat edges. That is, if a $C^{1}$ one-parameter family in this class passing through the stadium preserves the length spectrum, then its deformation function at the stadium vanishes identically. For flat edges of arbitrary length, the deformation functions of such families still span a finite-dimensional space.
