Inverse spectral problem for analytic plane domains I: Balian-Bloch trace formula

近简并轨道的 Balian–Bloch 波不变量

Balian-Bloch Wave Invariants for Nearly Degenerate Orbits

本文研究平面台球的波迹奇异支集与长度谱差异，通过近简并 Poincaré 映射周期轨道推导 Balian–Bloch 正则化预解式渐近迹公式，并分析 Maslov 指标与系数抵消。

Inverse spectral problem for analytic plane domains II: $\Z_2$-symmetric domains

This is part of a series of papers on the inverse spectral problem for bounded analytic plane domains. Here, we use the trace formula established in the first paper (`Balian-Bloch trace formula') to explicitly calculate wave trace invariants associated to bouncing ball orbits and dihedral rays. We use these invariants to prove that simply connected bounded analytic plane domains with one symmetry (which reverses a bouncing ball orbit of fixed length L) are spectrally determined in this class.

波迹中的静默轨道与抵消现象

Silent Orbits and Cancellations in the Wave Trace

该研究构造了含多条等长异Maslov指标周期弹球轨道的凸平面区域，通过微局部参数化子求解曲率射流方程组实现波迹抵消，证明波迹可任意光滑，揭示逆谱问题的局限及拉普拉斯谱与长度谱的本质差异。