发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究凹边界紧致曲面上台球流的擦碰闭轨迹，在非退化条件下计算正则化拉回的迹，推广了Atiyah-Bott-Guillemin迹公式。
AI 中文摘要
我们研究了紧致曲面$(\Sigma,g)$上具有凹边界的台球流$\varphi^t$的擦碰闭轨迹。在非退化条件下（例如当$(\Sigma,g)$具有负截面曲率时满足），我们计算了正则化拉回$E_{\epsilon}(\varphi^t)^* E_{\epsilon}$在单次擦碰闭轨迹附近的迹，这是Atiyah--Bott--Guillemin迹公式对闭台球轨迹的类比。
英文摘要
We study grazing closed trajectories of the billiard flow $φ^t$ on a compact surface $(Σ,g)$ with concave boundary. Under a non-degeneracy condition, which is satisfied for example when $(Σ,g)$ has negative sectional curvature, we compute the trace of a regularized pullback $E_ε(φ^t)^* E_ε$ near a closed trajectory grazing once, which is an analogue of the Atiyah--Bott--Guillemin trace formula for closed billiard trajectories.
Comments55 pages, 8 figures
