Spectral determination of analytic axi-symmetric plane domains

具有轴对称性的解析混沌台球的标记长度谱判定

Marked Length Spectral determination of analytic chaotic billiards with axial symmetries

本文研究具有轴对称性的解析混沌台球，利用非逃逸轨道与子移位的共轭关系标记周期轨道，证明在适当对称性与一般性条件下标记长度谱可唯一确定台球桌几何。

Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifolds

In this paper, the elastic Dirichlet-to-Neumann map $Ξ_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(Ω,g)$ with smooth boundary $\partial Ω$. By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map $Ξ_g$. We prove that for a strong convex or extendable real-analytic manifold with boundary, the elastic Dirichlet-to-Neumann map $Ξ_g$ uniquely determines the metric $g$ of $Ω$ in the sense of isometry, thereby solving an open problem for the uniqueness of the metric under real-analytic s…