你可以听到台球桌的形状:平面的象征性动态和刚性

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2018-04-16 DOI:10.4171/cmh/516

M. Duchin, V. Erlandsson, C. Leininger, C. Sadanand

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引用次数: 12

摘要

我们给出了欧几里得多边形的形状与其台球流的符号动力学之间关系的完整刻画。我们证明了唯一可以具有相同反弹谱的表对是不同于仿射映射的直角表。主要工具是一个新的定理，它证明了平锥度量完全由其刘维尔流的支持来确定。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces

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.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.