Hearing the shape of right triangle billiard tables

Author:

Shen Yang,Yang Jiazhong

Abstract

<p style='text-indent:20px;'>In this paper, we give a positive answer to the problem that whether one can identify the shape of a right triangle billiard table by a single bounce sequence. Moreover, a convenient method to calculate the shape of polygons is given in this paper, too.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference15 articles.

1. J. Bobok, S. Troubetzkoy.Does a billiard orbit determine its (polygonal) table?, Fundamenta Mathematicae, 212 (2011), 129-144.

2. J. Bobok, S. Troubetzkoy.Code and order in polygonal billiards, Topology and its Applications, 159 (2012), 236-247.

3. A. Calderon, S. Coles, D. Davis, J. Lanier and A. Oliveira, How to hear the shape of a billiard table, preprint, arXiv: 1806.09644, 2018.

4. M. Duchin, V. Erlandsson, C. J. Leininger and C. Sadanand, You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces, preprint, arXiv: 1804.05690, 2019.

5. G. Galperin.Non-periodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons, Comm. Math. Phys., 91 (1983), 187-211.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Anomalous dynamics in symmetric triangular irrational billiards;Physica D: Nonlinear Phenomena;2023-03

2. Hearing the shape of right triangle billiard tables;Discrete & Continuous Dynamical Systems;2021

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