你能听出台球的形状：平面曲面的符号动力学与刚性
几何拓扑
2019-10-17 v4 动力系统
摘要
我们给出了欧几里得多边形形状与其台球流符号动力学之间关系的完整刻画。我们证明，唯一可能具有相同反弹谱的台球桌对是相差一个仿射映射的直角台球桌。主要工具是一个新定理，该定理确立了平坦锥度量完全由其 Liouville 流的支持所决定。
引用
@article{arxiv.1804.05690,
title = {You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces},
author = {Moon Duchin and Viveka Erlandsson and Christopher J. Leininger and Chandrika Sadanand},
journal= {arXiv preprint arXiv:1804.05690},
year = {2019}
}
备注
v2: Updated language and references, including a reference for the flat strip theorem. v3: Added a section describing how the bounce spectrum can be determined given the countable set of bounce sequences of generalized diagonals. v4: Stylistic edits