期刊
COMMENTARII MATHEMATICI HELVETICI
卷 96, 期 3, 页码 421-463出版社
EUROPEAN MATHEMATICAL SOC-EMS
DOI: 10.4171/CMH/516
关键词
Billiards; surfaces; Euclidean; cone metric; Liouville current; symbolic dynamics
类别
资金
- NSF CAREER award [DMS-1255442]
- Academy of Finland [297258]
- NSF [DMS 1107452, 1107263, 1107367]
- Einstein Institute of Mathematics, Hebrew University
This study provides a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow, showing that only pairs of right-angled tables that differ by an affine map can have the same bounce spectrum. The main tool used in the study is a new theorem that establishes the complete determination of a flat cone metric by the support of its Liouville current.
We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tables that can have the same bounce spectrum are right-angled tables that differ by an affine map. The main tool is a new theorem that establishes that a flat cone metric is completely determined by the support of its Liouville current.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据